id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,470 | AMR-129-0005 | Billiards and Quantitative Symplectic Geometry — Johanna Bimmermann — Problem 1 | **Question:.** \begin{center}
Let $(N,g)$ be an orientable closed hyperbolic surface.\\ Does $c_{\mathrm{HZ}}\bigl(D^{*}N,d\lambda\bigr)<\infty$ hold?
\end{center}
We included the word ``orientable'' for the following reason. If the Euler
characteristic $\chi(N)$ is divisible by $4$ and $N$ is non-orientable,
then the... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Johanna Bimmermann — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Johanna Bimmermann | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,471 | AMR-129-0006 | Billiards and Quantitative Symplectic Geometry — Johanna Bimmermann — Problem 2 | **Question:.** \begin{center}
Is there a sequence of embedded billiard tables
$\Omega_i\subset N$, $i\in\mathbb{N}$, such that
$$
\Omega_i\text{-}\mathrm{sys}\longrightarrow \infty \quad \text{as } i\to\infty\ ?
$$
\end{center}
A positive answer would, to the best of the author’s knowledge, give the first example of a ... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Johanna Bimmermann — Problem 2
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Johanna Bimmermann | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,472 | AMR-129-0007 | Billiards and Quantitative Symplectic Geometry — Boris Khesin — Problem 1 | **1. Find physically interesting examples of infinite-dimensional billiards**
**Motivation:**
It is a well-known folklore (made into a theorem under certain conditions) that billiard and geodesic flows are closely related by taking appropriate limits, see e.g. [Giannetto, Lange]. There are various physical problems le... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Boris Khesin — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Boris Khesin | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,473 | AMR-129-0008 | Billiards and Quantitative Symplectic Geometry — Boris Khesin — Problem 2 | **3. Is there a fluid of negative density?**
**Motivation:** A mild reformulation of the question above is as follows: *Study continuous versions for the interactions of particles of positive and negative mass. Explore the relation with pseudo-Euclidean metrics.*
To motivate this question, we start with the motion of... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Boris Khesin — Problem 2
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Boris Khesin | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,474 | AMR-129-0009 | Billiards and Quantitative Symplectic Geometry — Jean-Fran\c{c — Problem 1 | **Problem statement** Let $M$ be a closed manifold that is not a $K(\pi,1)$, and endow the cotangent bundle $T^*M$ with its standard symplectic form. We conjecture that, for any closed and connected hypersurface $\Sigma\subset T^*M$ and any Hamiltonian $H:T^*M\to\mathbf{R}$ that admits $\Sigma$ as a regular energy leve... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Jean-Fran\c{c — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Jean-Fran\c{c | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,475 | AMR-129-0010 | Billiards and Quantitative Symplectic Geometry — Olga Paris-Romaskevich — Problem 1 | **Tiling billiards.**
A tiling billiard is a dynamical system associated with a plane polygonal tiling. Here is the rule: a particle moves in a straight line until it reaches an edge of a polygon; then it crosses into a neighboring polygon with its velocity direction changed according to Snell's law of refraction with ... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Olga Paris-Romaskevich — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Olga Paris-Romaskevich | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,476 | AMR-129-0011 | Billiards and Quantitative Symplectic Geometry — Olga Paris-Romaskevich — Problem 2 | **Two questions.**
In the following, I ask two questions, related in spirit -- one general and one specific. | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Olga Paris-Romaskevich — Problem 2
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Olga Paris-Romaskevich | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,477 | AMR-129-0012 | Billiards and Quantitative Symplectic Geometry — Olga Paris-Romaskevich — Problem 3 | \begin{question} In the class of tiling billiards in periodic tilings, is there a finite list of generic archetypal behaviors? For instance, the tiling billiards for which generic behavior is understood fall into one of two categories: either their typical trajectories are dense in open sets of the plane, as in cases 1... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Olga Paris-Romaskevich — Problem 3
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Olga Paris-Romaskevich | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,478 | AMR-129-0013 | Billiards and Quantitative Symplectic Geometry — Alfonso Sorrentino — Problem 1 | **Problem:** *Provide examples of real-world systems (from physics, mechanics, biology, economics, etc\ldots) that can be modeled as locally conformal symplectic flows or maps.*
In the following, we provide some material that could be useful to address this question. We begin by recalling the formal setting, starting ... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Alfonso Sorrentino — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Alfonso Sorrentino | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,479 | AMR-129-0014 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 1 | **Projective billiards..** Projective billiards were defined in [Ta97]. A projective billiard table is a convex domain with smooth boundary equipped with a transverse field of directions; the phase space is the same as that of the conventional billiard, and the reflection law is such that the tangential component of th... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,480 | AMR-129-0015 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 2 | **Inner and outer periodic orbits on immersed submanifolds..** Let $M$ be a closed immersed submanifold of Euclidean space. A generalized $n$-periodic billiard trajectory is an $n$-gon inscribed in $M$ (that is, the vertices lie on $M$) that has an extremal perimeter.
Problem: *estimate from below the number of $n$-pe... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 2
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,481 | AMR-129-0016 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 3 | **Complexity of polygonal symplectic billiards..** Symplectic billiards were introduced in [AT]; the polygonal ones were studied in [ABSST,ALW].
Label the sides of a polygon by some symbols and assign to a billiard trajectory its symbolic code, the corresponding bi-infinite word in these symbols. The set of all trajec... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 3
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,482 | AMR-129-0017 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 4 | **Chaotic symplectic billiards?.** Problem: *do chaotic symplectic billiards in convex $C^1$-smooth domains exist?*
A natural candidate is the stadium; there is numerical evidence that this might be the case. | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 4
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,483 | AMR-129-0018 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 5 | **Planar characteristic curves..** Let $M$ be (a germ of) a smooth hypersurface in the standard symplectic space.
Problem: *how restrictive is the condition that the characteristic curves on $M$ are planar?*
If $M$ is closed and convex, the situation is rigid: $M$ is an affine symplectic image of a round ball; see [K... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 5
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,484 | AMR-129-0019 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 6 | **Density of reflected wave fronts..** Consider a domain with smooth boundary in Euclidean space and let $P$ be a generic point in its interior. Let $P$ be a source of light, and consider the time $t$-front, that is, the locus of ``photons" emanating from $P$ in all directions, undergoing optical reflection off the bou... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 6
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,485 | AMR-129-0020 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 7 | **Ivrii's conjecture for outer symplectic billiards..** The Ivrii conjecture for conventional billiards asserts that the set of periodic orbits has zero measure (with respect to the measure associated with the invariant symplectic structure of the phase space). A similar conjecture applies to the outer symplectic billi... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 7
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,486 | AMR-129-0021 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 8 | **Approximating a convex curve by polygons with respect to the symmetric difference..** A popular topic in convex geometry is the approximation of smooth convex closed curves by polygons, see [Gr]. The quality of approximation by $n$-gons may be measured by the difference of perimeters or areas, and the polygons may be... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 8
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,487 | AMR-129-0022 | Billiards and Quantitative Symplectic Geometry — Serge Tabachnikov — Problem 9 | **Optical transformations of the space of oriented lines..** The billiard (optical) reflection is a (local) symplectic transformation of the space of oriented lines (rays of light); this space carries a symplectic structure induced by the canonical symplectic structure of the cotangent bundle of the ambient $n$-dimensi... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Serge Tabachnikov — Problem 9
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Serge Tabachnikov | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,488 | AMR-129-0023 | Billiards and Quantitative Symplectic Geometry — Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 1 | **Conjecture 1.** For a Reeb flow on a closed connected $3$-manifold, either there are exactly two periodic orbits, or $$ \liminf_{T\to+\infty} \frac{\log P(T)}{\log T} \geq 2 $$ holds.
The conjecture above, which is also cited in [DanCG], has been confirmed in [Albach] for geodesic flows of reversible Finsler metrics... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 1
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Be... | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,489 | AMR-129-0024 | Billiards and Quantitative Symplectic Geometry — Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 2 | **Problem 1.** Is it true that for a Hamiltonian diffeomorphism on a closed symplectic manifold, either the number of periodic orbits is finite, or periodic orbits grow at least quadratically in the sense that $\liminf_{T\to+\infty} \frac{\log P(T)}{\log T} \geq 2$?
Due to the lack of counterexamples, we suspect the a... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 2
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Be... | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,490 | AMR-129-0025 | Billiards and Quantitative Symplectic Geometry — Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 3 | **Problem 2.** Is it true that $\liminf_{T\to+\infty} \frac{\log P(T)}{\log T} \geq 2$ holds for every Hamiltonian diffeomorphism on a standard symplectic torus? Or in an arbitrary aspherical closed symplectic manifold? | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 3
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Be... | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,491 | AMR-129-0026 | Billiards and Quantitative Symplectic Geometry — Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 4 | **Problem 3.** Is it true that for a Hamiltonian diffeomorphism on $\mathbf{C}P^n$ with infinitely many periodic orbits the inequality $\liminf_{T\to+\infty} \frac{\log P(T)}{\log T} \geq 2$ holds?
In low-dimensions, integrable Hamiltonian systems indicate that quadratic growth should be sharp. To justify this, if one... | Source list: Albach, Barraud et al. - Open Problems in Billiards and Quantitative Symplectic Geometry (2026)
Source item: Bernhard Albach, Umberto Hryniewicz, and Alexandru Oancea — Problem 4
Source URL: https://arxiv.org/abs/2602.12896
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Contributor: Be... | 3 | open | Albach, Barraud et al. | 2,026 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,492 | AMR-130-0001 | Linear Systems and Eigenvalue Problems — Problem 1 | We propose focusing the benchmark problems on linear systems that
are discretizations of partial differential
equations (PDEs) due to both their wide application in science and
engineering and to their connection to graph Laplacians that have
been a focus of TCS research in linear system solvers.
Furthermore, matrix co... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,493 | AMR-130-0002 | Linear Systems and Eigenvalue Problems — Problem 2 | For each class of parameterized benchmark linear systems, develop
theoretically and practically fast algorithms. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,494 | AMR-130-0003 | Linear Systems and Eigenvalue Problems — Problem 3 (Algebraic Multigrid Analysis for Theoretical Computer Scientists) | Show that for polynomially bounded SWCDDM matrices $\mathbf{M}$,
Algebraic Multigrid runs in time $\tilde{O}(\operatorname{nnz}(\mathbf{M}))$ to compute an (implicitly represented) symmetric matrix $\mathbf{Z}$,
which can be applied in $O(\operatorname{nnz}(\mathbf{M}))$ time, and satisfies the condition that
$ \Omega(... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Algebraic Multigrid Analysis for Theoreti... | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,495 | AMR-130-0004 | Linear Systems and Eigenvalue Problems — Problem 4 (Polynomially decaying eigenvalues) | Fix constants $\varepsilon > 0$ and $p > 0$.
Let $\mathbf{A}_n \in \mathbb{C}^{n \times n}$, $n\geq 1$, be a sequence of random positive definite matrices constructed via
\begin{equation*}
\mathbf{A}_n = \mathbf{U} \mathbf{\Lambda}_n \mathbf{U}^*,
\quad \text{where } \begin{cases} \mathbf{U} \in \mathbb{C}^{n \times n}... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Polynomially decaying eigenvalues | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,496 | AMR-130-0005 | Linear Systems and Eigenvalue Problems — Problem 5 | *Complexity for sparse matrices.* Importantly, the matrix-vector product model is most relevant for sparse matrices, in which case the extra cost paid by the Krylov solver is only $\tilde O(\mathrm{nnz}(A)\cdot k)$, where $\mathrm{nnz}(A)$ is the number of non-zero entries in $A$ (although, importantly, additional cost... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,497 | AMR-130-0006 | Linear Systems and Eigenvalue Problems — Problem 6 | Find the smallest $p>0$ such that we can solve an $n\times n$ linear system $Ax=b$ to high accuracy using $\tilde O(\mathcal{T}_A\cdot\bar\kappa_p)$ arithmetic operations, where $\bar\kappa_p$ is the $p$-averaged condition number of the singular values of $A$, whereas $\mathcal{T}_A$ is either $n^2$ or $\mathrm{nnz}(A)... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,498 | AMR-130-0007 | Linear Systems and Eigenvalue Problems — Problem 7 | What is the complexity of solving $(n,0,l,\kappa)$ linear systems, and how is this affected by the model of computation (direct access vs matrix-vector product)? | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,499 | AMR-130-0008 | Linear Systems and Eigenvalue Problems — Problem 8 | Let $A$ be an $n\times n$ random matrix with i.i.d. Gaussian (or Rademacher, or Bernoulli) entries, and take any $n$-dimensional vector $b$. Is it possible (conditioned on a high-probability event) to solve the linear system $Ax=b$ to high accuracy faster than $O(n^\omega)$? | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 8
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,500 | AMR-130-0009 | Linear Systems and Eigenvalue Problems — Problem 9 | What is the bit complexity of solving $(n,k,l,\kappa)$ linear systems? In particular, does the $\tilde O(k^\omega + n^2\kappa)$ running time for $(n,k,0,\kappa)$ systems extend to the Word-RAM model? | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,501 | AMR-130-0010 | Linear Systems and Eigenvalue Problems — Problem 10 | What is the bit complexity of solving an $n\times n$ linear system with $\text{nnz}(A)$ non-zeros? In particular, does the $\tilde O(n\cdot \text{nnz}(A))$ runtime extend to the Word-RAM model. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,502 | AMR-130-0011 | Linear Systems and Eigenvalue Problems — Problem 11 | Another reason for focusing on condition number reduction rather than ``improving'' the entire eigenvalue distribution by preconditioning is that the eigenvalue distribution is usually unknown in practical applications. Yet, the recent line of work in [GerMadNieStr19,GerNieStr20,GerNieStr22,NieStr24] has shown that for... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,503 | AMR-130-0012 | Linear Systems and Eigenvalue Problems — Problem 12 | The behavior of iterative methods such as GMRES for solving nonsymmetric (more precisely, nonnormal) linear algebraic systems is much less understood than the behavior of CG. In general, the performance in this case may depend not only on the eigenvalue distribution, but also on further quantities including the conditi... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,504 | AMR-130-0013 | Linear Systems and Eigenvalue Problems — Problem 13 | Find an interesting (nonselfdajoint resp. nonsymmetric) model problem, where the theoretical result on the eigenvalue distribution of the preconditioned matrix indeed corresponds to the actual convergence behavior of GMRES (e.g., $M^{-1}A$ has $m$ eigenvalue clusters and an acceptable approximate solution is obtained b... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,505 | AMR-130-0014 | Linear Systems and Eigenvalue Problems — Problem 14 | Explain the convergence acceleration of GMRES after the initial (transient) phase that is observed in some convection-diffusion model problems such as the one in [LieStr05]. In particular, explain whether or not the speed of convergence can be related to eigeninformation (i.e., eigenvalue location and eigenvector condi... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,506 | AMR-130-0015 | Linear Systems and Eigenvalue Problems — Problem 15 | A number of methods for solving linear systems (with or without a preconditioner) can be implemented in the following form: Starting with an initial guess $x_0$ for the solution to $Ax=b$, for $k=1,2, \ldots$,
set
\begin{eqnarray*}
x_k & = & x_{k-1} + a_{k-1} p_{k-1} \\
r_k & = & r_{k-1} - a_{k-1} A p_{k-1} .
\end{eqna... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 15
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,507 | AMR-130-0016 | Linear Systems and Eigenvalue Problems — Problem 16 | Show that the CG and Lanczos algorithms do or do not behave similarly in finite precision arithmetic when used to solve a symmetric positive definite linear system. This will, of course, depend on the implementation of each method, so use standard good implementations of both. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 16
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,508 | AMR-130-0017 | Linear Systems and Eigenvalue Problems — Problem 17 | How many bits of precision are necessary to guarantee that CG applied to an $n$ by $n$ SPD linear system $Ax=b$ obtains an approximate solution with normwise backward error at most $\epsilon$ in $n$ (or fewer) steps? | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 17
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,509 | AMR-130-0018 | Linear Systems and Eigenvalue Problems — Problem 18 | Analyze the Lanczos algorithm under general models of inexact matrix-vector multiplication and/or the use of a preconditioner.
Progress is made if these bounds generalize Paige's analysis and/or provide new, easier to understand, insight into the behavior of the algorithm. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 18
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,510 | AMR-130-0019 | Linear Systems and Eigenvalue Problems — Problem 19 | Extend Paige's analysis of the Lanczos algorithm [paige_76,paige_80] to the block Lanczos algorithm.
The exact analysis will depend on the use of an orthogonalization scheme used within blocks, so either specify certain assumptions on the accuracy of the scheme, or analyze a standard ``good'' algorithm. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 19
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,511 | AMR-130-0020 | Linear Systems and Eigenvalue Problems — Problem 20 (Deterministic Pseudospectral Shattering) | Give a provably correct and efficient *deterministic* algorithm for the following task: on input $A\in\mathbb{C}^{n\times n}$ and $\delta>0$, output a perturbation $E$ with $\|E\|\le \delta$ such that $\kappa_{eig}(A+E)\le C(\delta/n)^c$,
where $C,c$ are universal constants.
In this context, efficient means $O(n^3\log^... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 20
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Deterministic Pseudospectral Shattering | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,512 | AMR-130-0021 | Linear Systems and Eigenvalue Problems — Problem 21 (Deterministic Minami Perturbation) | Minami [minami1996local] showed that if $A$ is $n\times n$ Hermitian tridiagonal and $E$ is a random diagonal matrix with independent absolutely continuous entries, then $gap(A+\delta E)\ge C(\delta/n)^c$ for some constants $C,c$ depending on the distribution of the entries. Give an efficient deterministic algorithm fo... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 21
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Deterministic Minami Perturbation | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,513 | AMR-130-0022 | Linear Systems and Eigenvalue Problems — Problem 22 | We propose the following problem, which will improve the result in [Banks-et-al-23] (for diagonalization) and in [banks2022global] (for the Schur form). The motivation is that the amount of precision required by the best currently known provable algorithms for diagonalization/Schur form is much larger than the gold sta... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 22
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,514 | AMR-130-0023 | Linear Systems and Eigenvalue Problems — Problem 23 | For a given $A\in{\mathbb{C}}^{n\times n}$, let $\widehat{\mathcal{V}$ denote an approximate invariant subspace of dimension $d$ of $A$, in the sense that there exists some $d$-dimensional invariant subspace ${\mathcal{V}$ of $A$ such that $\angle({\mathcal{V},\widehat{\mathcal{V})$ is small.
Let ${\mathcal{W}$ be some... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 23
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,515 | AMR-130-0024 | Linear Systems and Eigenvalue Problems — Problem 24 | Let $Q$ be an orthonormal basis for a Krylov space for arbitrary $A\in{\mathbb{C}}^{n\times n}$ with random starting vector $b$. Is $\kappa_V(Q^*AQ)$ bounded (by a polynomial in $n$) with high probability? Or is ${\mathbb{E}}[\operatorname{area}\Lambda_\varepsilon(Q^*AQ)]$ (the expected value of the area in ${\mathbb{C... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 24
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,516 | AMR-130-0025 | Linear Systems and Eigenvalue Problems — Problem 25 | Consider a non-Hermitian $A\in{\mathbb{C}}^{n\times n}$ and suppose $Q\in{\mathbb{C}}^{n\times k}$ has orthonormal columns. We know that the Ritz values (eigenvalues of $Q^*AQ$) are located in the numerical range, $W(A) = \{v^*Av: \|v\|_2=1\}$, a closed, convex subset of ${\mathbb{C}}$ that contains the eigenvalues of ... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 25
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,517 | AMR-130-0026 | Linear Systems and Eigenvalue Problems — Problem 26 | There is currently no rigorous proof (in the vein of theoretical computer science) of success for a floating-point implementation of MR$^3$ when applied to an arbitrary symmetric tridiagonal matrix. Willems and Lang [Willems_framework] have given a proof of correctness which is conditional on several underlying assumpt... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 26
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,518 | AMR-130-0027 | Linear Systems and Eigenvalue Problems — Problem 27 | Let $B$ be an $n \times n$ (upper) bidiagonal matrix. Is there an algorithm that, in $O(kn)$ operations, can produce $k$ triples $(\sigma_i,v_i,u_i)$ such that $\sigma_i \geq 0$, $v_i, u_i \in {\mathbb{C}}^n$ are unit vectors, and, for machine precision $\epsilon$,
- $\|Bv_i-\sigma_iu_i\|_2 = O(\epsilon n\|B\|_2)$;
-... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 27
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,519 | AMR-130-0028 | Linear Systems and Eigenvalue Problems — Problem 28 | Consider a general nonnormal matrix $A = V \Lambda V^{-1}$ with largest eigenvalue magnitude $\lambda_1$ and finite eigenvector condition number $\kappa_V = \|V\| \|V^{-1}\|$.
Is there an algorithm that uses $\mathrm{poly}(\log(n\kappa_V),1/\epsilon)$ matrix-vector products with $A$ and returns $\lambda$ so that $|\lam... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 28
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,520 | AMR-130-0029 | Linear Systems and Eigenvalue Problems — Problem 29 | Prove stronger theoretical bounds for GECP applied to $K$, by exploiting the structure of the kernel $K$. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 29
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,521 | AMR-130-0030 | Linear Systems and Eigenvalue Problems — Problem 30 | It is known that there exists $I$ such that $\|Q(I,:)^{-1}\|_2 \le \sqrt{k(n-k+1)}$ [hong1992rank] and there is a fairly efficient $O(nk^2)$ algorithm that satisfies this bound [Osinsky2025close].
Does the QRCP algorithm typically used in practice satisfy the above, or a similar, bound. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 30
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,522 | AMR-130-0031 | Linear Systems and Eigenvalue Problems — Problem 31 | Consider selecting $r = \mathcal{O}(k)$ uniformly random row indices $I$ and then choosing column indices $\tilde{J}$ so that $A(I,:) \approx A(I,\tilde{J}) \tilde{T}$.
What are sufficient conditions on $r$ and on the kernel $f$ which guarantee that
\begin{equation}
\|\Pi_{\tilde{J}} A - A\|_F \leq c(n, m, k) \|\Pi_J A... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 31
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,523 | AMR-130-0032 | Linear Systems and Eigenvalue Problems — Problem 32 | Consider $n$ positive real numbers $\lambda$, and consider the set of all $n \times n$ orthonormal matrices $S$.
Prove a tightness bound(s) between the (1) trace error of the optimal column subset selection of the worst case matrix $K$ possessing eigenvalues $\lambda$:
\begin{equation}
x_k (\lambda) := \max_{V \in S} \... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 32
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,524 | AMR-130-0033 | Linear Systems and Eigenvalue Problems — Problem 33 (Sketch-and-solve) | Let \(A \in \mathbb{R}^{n \times d}\) be a full-rank matrix, \(B\in\mathbb{R}^{n \times p}\) be a matrix, and let \(\Omega \in \mathbb{R}^{n \times k}\) be an oblivious subspace injection with dimension $d$ and injectivity \(1-\varepsilon\).
Let \(\tilde X = (\Omega^\top A)^+(\Omega^\top B) \in \mathbb{R}^{d \times p}\... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Sketch-and-solve | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,525 | AMR-130-0034 | Linear Systems and Eigenvalue Problems — Problem 34 (Randomized SVD) | Let \(A \in \mathbb{R}^{n \times d}\) be a matrix, fix $r > 0$, and let \(\Omega \in \mathbb{R}^{n \times k}\) be an oblivious subspace injection with dimension $r$ and injectivity \(1-\varepsilon\).
Let $\tilde{A} = (A\Omega)(A\Omega)^+A$ denote the randomized SVD approximation to $A$, and let $A_r$ be the best rank-$... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 34
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Randomized SVD | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,526 | AMR-130-0035 | Linear Systems and Eigenvalue Problems — Problem 35 (Regression in the $\ell_p$ norm) | Consider the $\ell_p$ linear regression problem
\begin{equation*}
\operatorname{minimize}_{x \in\mathbb{R}^d} \|Ax - b\|_{\ell_p}
\end{equation*}
for a matrix \(A \in \mathbb{R}^{n \times d}\) and a vector \(b\in\mathbb{R}^{n}\).
For a sketching matrix \(\Omega \in \mathbb{R}^{n \times k}\), the sketch-and-solve solu... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Regression in the $\ell_p$ norm | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,527 | AMR-130-0036 | Linear Systems and Eigenvalue Problems — Problem 36 | Prove or disprove the Nelson--Nguyen conjecture: A SparseStack embedding with parameters $\zeta = \mathcal{O}((\log r) / \varepsilon)$ and $k = \mathcal{O}(r / \varepsilon^2)$ is an oblivious subspace embedding with parameters $\alpha = 1 - \varepsilon$ and $\beta = 1+\varepsilon$. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Nelson--Nguyen conjecture: Subspace embe... | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,528 | AMR-130-0037 | Linear Systems and Eigenvalue Problems — Problem 37 (Subspace injection properties of sparse random matrices) | Assume the condition $r\le \mathcal{O}(n/\log n)$ relating the subspace dimension $r$ and the ambient dimension $n$.
Prove or disprove: A SparseStack embedding with parameters $\zeta = \mathcal{O}(1)$ and $k = \mathcal{O}(r)$ is an oblivious subspace injection with parameter $\alpha = \mathrm{const}$.
More specifically... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 37
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Subspace injection properties of sparse ... | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,529 | AMR-130-0038 | Linear Systems and Eigenvalue Problems — Problem 38 (Rerandomized subsampled trigonometric transforms) | Assume that $n = \Omega(\log r)$.
Prove or disprove: The rerandomized SRHT of dimension $k = \mathcal{O}(r/\varepsilon^2)$ is an oblivious subspace embedding with $\alpha = 1-\varepsilon$ and $\beta = 1+\varepsilon$. | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 38
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Rerandomized subsampled trigonometric tr... | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,530 | AMR-130-0039 | Linear Systems and Eigenvalue Problems — Problem 39 | Given any choice of $m$-node tree tensor network (e.g., tensor train or Tucker) and choice of ranks (dimensions of edges in the tensor network), let the set of representable tensors in this tensor network be $S\subset \mathbb{R}^{d_1\times \cdots \times d_n}$.
Find a polynomial-time algorithm that takes as input any te... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 39
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,531 | AMR-130-0040 | Linear Systems and Eigenvalue Problems — Problem 40 | Let $\Pi_{2^m}^*$ be the set of univariate polynomials whose corresponding matrix function can be computed with $m$ matrix-matrix multiplications and an arbitrary number of matrix additions and scalings.
We consider the problem of determining the best such polynomial that approximates the sign function in $I:=[-1,-\del... | Source list: Amsel, Baumann et al. - Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026)
Source item: Problem 40
Source URL: https://arxiv.org/abs/2602.05394
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Amsel, Baumann et al. | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,532 | AMR-131-0001 | Visibility Graphs of Points, Segments and Polygons — Problem 1 | We have stated earlier how to compute the visibility graph $G$ from a given set of
points $P$. Consider the opposite problem of determining if there is a set of points $P$
whose visibility graph is the given graph $G$. This problem is called the visibility graph
*recognition* problem. Identifying the set of properties ... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,533 | AMR-131-0002 | Visibility Graphs of Points, Segments and Polygons — Problem 2 | \begin{unsolved}
Given a graph $G$ in adjacency matrix form, determine whether $G$ is the visibility graph of a set
of points $P$ in the plane.
\end{unsolved}
Characterize visibility graphs of point sets. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,534 | AMR-131-0003 | Visibility Graphs of Points, Segments and Polygons — Conjecture 4 | For all integers $k \geq 2$ and $\ell \geq 2$, there is an integer $h(k,\ell)$ such that any
point set $P$ of at least $h(k,\ell)$ points in the plane contains
$\ell$ collinear points, or $k$ mutually visible points. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Conjecture 4
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,535 | AMR-131-0004 | Visibility Graphs of Points, Segments and Polygons — Problem 5 | Let us discuss upper bounds on $b(n)$. It is obvious that $b(n) \leq {n \choose 2}$. Let
$\mu(P)$ denote the size of the set of midpoints of all ${n \choose 2}$ segments between points
of $P$. Let $\mu(n)$ denote the minimum of $\mu(P)$ for all $P$ having $n$ points with no
three points being collinear. Using Freiman's... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,536 | AMR-131-0005 | Visibility Graphs of Points, Segments and Polygons — Conjecture 6 | In every $k$-blocked point set, there are at most $k$ points in each colour class. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Conjecture 6
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,537 | AMR-131-0006 | Visibility Graphs of Points, Segments and Polygons — Problem 7 | Consider the problem of obstacle representation of a given graph $G$ of $n$ vertices, which was
introduced by Alpet et al. [akl-ong-2010]. Draw
every vertex $v_i$ of $G$ as a point $p_i$ in the plane and draw obstacles in such a way
that every segment $p_ip_j$
intersects an obstacle if and only if $(v_i,v_j)$ is not an... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,538 | AMR-131-0007 | Visibility Graphs of Points, Segments and Polygons — Problem 8 | Regarding the lower bound on obstacle numbers,
Alpet et al. [akl-ong-2010] have showed that there exists a graph of $n$ vertices with
obstacle number $O(\sqrt{\log n})$, which has been improved
to $O(n/\log ^2 n)$ by Mukkamala et al. [mps-glon-2010]. The bound becomes $O(n/\log n)$
if the obstacles are restricted to co... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,539 | AMR-131-0008 | Visibility Graphs of Points, Segments and Polygons — Problem 9 | Regarding the graphs with low obstacle numbers,
Alpet et al. [akl-ong-2010]
and Mukkamala et al. [mps-glon-2010] have studied graphs with obstacle numbers
$1$ and $2$. Mukkamala et al. [mps-glon-2010] showed that for any positive integer $h \geq 3$,
there is a graph with obstacle number exactly $h$. The following quest... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,540 | AMR-131-0009 | Visibility Graphs of Points, Segments and Polygons — Problem 10 | \begin{unsolved}
For $h>1$, what is the smallest number of vertices of a graph with obstacle number $h$?
\end{unsolved}
Does every planar graph have obstacle number $1$? | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,541 | AMR-131-0010 | Visibility Graphs of Points, Segments and Polygons — Problem 11 | All three above problems are open for segment visibility graphs.
Only characterization known is for a sub-class
given by Everette et al. [ehkn-cgta2-2000].
They have characterized those segment visibility graphs that do not have $K_5$ (a complete graph of
five vertices) as a minor. A graph $M$ is called a *minor* of a ... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,542 | AMR-131-0011 | Visibility Graphs of Points, Segments and Polygons — Problem 12 | \begin{unsolved}
Given a graph $G$ in adjacency matrix form, determine whether $G$ is the segment visibility graph
of a set of disjoint segments $S$ in the plane.
\end{unsolved}
Characterize the segment visibility graphs. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 12
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,543 | AMR-131-0012 | Visibility Graphs of Points, Segments and Polygons — Conjecture 14 | {
(a) The cycle $C=(p_1, p_{10}, p_9, p_8, p_7, p_5, p_4, p_6, p_3, p_2, p_1)$ is Hamiltonian
but is self-intersecting.
(b) The cycle $C=(p_1, p_9, p_{10}, p_7, p_8, p_6, p_5, p_4, p_3, p_2, p_1)$ is a Hamiltonian
circuit as it forms a boundary of a simple polygon.
(c) There is no alternating cycle as both endpoints of... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Conjecture 14
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,544 | AMR-131-0013 | Visibility Graphs of Points, Segments and Polygons — Conjecture 15 | Every segment visibility graph $G$ contains a Hamiltonian cycle $C$ that corresponds to a
Hamiltonian circuit in the embedded segment visibility graph $G'$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Conjecture 15
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,545 | AMR-131-0014 | Visibility Graphs of Points, Segments and Polygons — Conjecture 16 | Every segment visibility graph $G$ contains a Hamiltonian cycle $C$ that corresponds to
the boundary of a circumscribing polygon in the embedded segment visibility graph $G'$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Conjecture 16
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,546 | AMR-131-0015 | Visibility Graphs of Points, Segments and Polygons — Problem 17 | Observe that the algorithm of Hoffmann and T\'{o}th [ht-sevg-2003] takes $S$ as an input
and then locates a Hamiltonian circuit in the embedded segment visibility graph $G'$.
Suppose $S$ is not given as an input but
only $G$ is given, then it is not clear how to identify a Hamiltonian cycle
in $G$ in polynomial time as... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 17
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,547 | AMR-131-0016 | Visibility Graphs of Points, Segments and Polygons — Problem 18 | \begin{unsolved}
Given a segment visibility graph $G$ in adjacency matrix form, identify a Hamiltonian
cycle in $G$ in polynomial time.
\end{unsolved}
Given a segment visibility graph $G$ in adjacency matrix form, identify the edges of
$G$ that correspond to segments of $S$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 18
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,548 | AMR-131-0017 | Visibility Graphs of Points, Segments and Polygons — Problem 19 | Let us consider variations of bar visibility graphs. While representing vertices of $G$ as
bars, there is no restriction on the length of horizontal bars. Suppose, a restriction
is imposed that all bars in a visibility representation must have the same length.
In that case, we get another type of visibility graphs whic... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 19
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,549 | AMR-131-0018 | Visibility Graphs of Points, Segments and Polygons — Problem 21 | Unlike bar visibility graphs,
bar $k$-visibility graphs have not been completely characterized. For understanding this
class of graphs, Dean et al. [deglst-bvg-2007] considered the problem of
bounding the number of edges of a bar $k$-visibility graph $G$. They proved an upper
bounds of $(k+1)(3n-7/2 k-5)-1$ edges
for $... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 21
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,550 | AMR-131-0019 | Visibility Graphs of Points, Segments and Polygons — Problem 23 | \begin{unsolved}
Triangle-free non-planar graphs are forbidden subgraphs of bar $k$-visibility graphs.
Is there any other class of forbidden subgraphs of bar $k$-visibility graphs?
\end{unsolved}
Are there $(2k+2)$-regular bar $k$-visibility graphs for $k \geq 5$? | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 23
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,551 | AMR-131-0020 | Visibility Graphs of Points, Segments and Polygons — Problem 25 | \begin{unsolved}
Are there $(2k+2)$-regular bar $k$-visibility graphs for $k \geq 5$?
\end{unsolved}
\begin{unsolved}
Are there $d$-regular bar $k$-visibility graphs with $d \geq 2k+3$?
\end{unsolved}
Improve the current upper bound of $6k+6$ on the chromatic number of a bar $k$-visibility graph. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 25
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,552 | AMR-131-0021 | Visibility Graphs of Points, Segments and Polygons — Problem 26 | Dean et al. [deglst-bvg-2007] also studied the thickness of bar $k$-visibility graphs.
The *thickness* of a graph $G$ is defined as the minimum number of planar graphs whose
union is $G$. Exact values of thickness is know for very few classes of graphs [mos-tgs-1998].
Dean et al. proved an upper bound of $4$ for the th... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 26
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,553 | AMR-131-0022 | Visibility Graphs of Points, Segments and Polygons — Problem 27 | The crossing number of a graph is the minimum possible number of crossings with which the graph
can be drawn in the plane.
What is the largest crossing number of a bar $k$-visibility graph? | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 27
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,554 | AMR-131-0023 | Visibility Graphs of Points, Segments and Polygons — Problem 28 | \begin{unsolved}
The crossing number of a graph is the minimum possible number of crossings with which the graph
can be drawn in the plane.
What is the largest crossing number of a bar $k$-visibility graph?
\end{unsolved}
The genus of a graph is the minimal integer $g$ such that the graph can be embedded on a surface ... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 28
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,555 | AMR-131-0024 | Visibility Graphs of Points, Segments and Polygons — Problem 29 | Bar visibility graphs have been generalized to rectangle visibility
graphs by considering both vertical and horizonal visibility among bars
having non-zero
thickness [bdhs-orvg-1997,dh-rvrbp-1997,o-opcv-1998,r-drvg-1997,sw-rvgc-2003].
A graph $G$ is called a *rectangle visibility graph* if it can be realized by closed ... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 29
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,556 | AMR-131-0025 | Visibility Graphs of Points, Segments and Polygons — Problem 30 | \begin{unsolved}
Given a graph $G$ in adjacency matrix form, determine whether $G$ is the visibility graph of a simple
polygon $P$.
\end{unsolved}
Is the problem of recognizing visibility graphs in $NP$? | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 30
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,557 | AMR-131-0026 | Visibility Graphs of Points, Segments and Polygons — Problem 31 | Given a graph $G$ in adjacency matrix form along with a Hamiltonian cycle $C$ of $G$,
determine whether $G$ is the visibility graph of a simple polygon $P$ whose boundary corresponds
to the given Hamiltonian cycle $C$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 31
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,558 | AMR-131-0027 | Visibility Graphs of Points, Segments and Polygons — Problem 32 | Design an algorithm for testing Necessary Condition 4 in polynomial time. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 32
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,559 | AMR-131-0028 | Visibility Graphs of Points, Segments and Polygons — Problem 33 | Draw a simple polygon whose visibility graph is the given graph $G$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 33
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,560 | AMR-131-0029 | Visibility Graphs of Points, Segments and Polygons — Problem 34 | A *Hamiltonian cycle* is a cycle in an undirected graph which visits each vertex exactly once
and also returns to the starting vertex. The Hamiltonian cycle problem is to determine whether a
Hamiltonian cycle exists in a given graph $G$. Observe that $G$ may contain
several Hamiltonian cycles, and $G$ may be visibility... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 34
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,561 | AMR-131-0030 | Visibility Graphs of Points, Segments and Polygons — Problem 35 | A *dominating set* for a graph $G = (V, E)$ is a subset $D$ of $V$ such that every vertex
not in $D$ is joined to at least one member of $D$ by some edge. The minimum dominating
set problem in visibility graphs corresponds to the art gallery problem in polygons which has been
shown to be NP-hard [ll-ccagp-86, ls-cavg-9... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 35
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,562 | AMR-131-0031 | Visibility Graphs of Points, Segments and Polygons — Problem 36 | Given the visibility graph $G$ of a simple polygon $P$ along with the Hamiltonian cycle in $G$
corresponding to the boundary of $P$, determine the maximum hidden set of $G$. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 36
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,563 | AMR-131-0032 | Visibility Graphs of Points, Segments and Polygons — Problem 37 | \begin{unsolved}
Given the visibility graph $G$ of a simple polygon $P$ along with the Hamiltonian cycle in $G$
corresponding to the boundary of $P$, determine the maximum hidden set of $G$.
\end{unsolved}
Design an approximation algorithm for computing maximum hidden set of visibility graph. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 37
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,564 | AMR-131-0033 | Visibility Graphs of Points, Segments and Polygons — Problem 38 | A *clique* in a graph is a set of pairwise adjacent vertices. The problem of computing the maximum
clique in the visibility graph is not known to be NP-hard. Observe that the maximum clique in a
visibility graph corresponds to the largest empty convex polygon inside the corresponding polygon.
Algorithms for computing l... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 38
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,565 | AMR-131-0034 | Visibility Graphs of Points, Segments and Polygons — Problem 39 | \begin{unsolved}
Given a visibility graph $G$ in adjacency matrix form, compute a maximum clique of $G$.
\end{unsolved}
Determine whether a set of vertices of a visibility graph has a triangle-extendible ordering in
polynomial time. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 39
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,566 | AMR-131-0035 | Visibility Graphs of Points, Segments and Polygons — Problem 40 | Two graphs $G_1 = (V_1, E_1)$ and $G_2 = (V_2, E_2)$ are *isomorphic* if and only if there
is a bijection $f$ that maps vertices of $V_1$ to the vertices of $V_2$ such that an edge
$(v, w) \in E_1$ if and only if the edge $(f(v), f(w)) \in E_2$. It has been shown
by Ghosh [g-vap-07] that the number of *non-isomorphic* ... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 40
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,567 | AMR-131-0036 | Visibility Graphs of Points, Segments and Polygons — Problem 41 | Although the most natural form of representation for visibility graphs would be to use coordinates
of the points, this is not useful if we are looking for a space efficient representation. Lin and
Skiena [ls-cavg-95] have proved that visibility graphs require endpoints to have
exponential sized integers. However, it is... | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 41
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,568 | AMR-131-0037 | Visibility Graphs of Points, Segments and Polygons — Problem 42 | Give a tight bound (with respect to order notation) on the number of bits used in an optimal
covering set of a visibility graph. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 42
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,569 | AMR-131-0038 | Visibility Graphs of Points, Segments and Polygons — Problem 43 | \begin{unsolved}
Give a tight bound (with respect to order notation) on the number of bits used in an optimal
covering set of a visibility graph.
\end{unsolved}
Find a covering set which matches the above bound in polynomial time. | Source list: Ghosh, Goswami - Unsolved Problems in Visibility Graphs of Points, Segments and Polygons (2010)
Source item: Problem 43
Source URL: https://arxiv.org/abs/1012.5187
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Ghosh, Goswami | 2,010 | 3 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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