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I'm trying to prove that a binary heap with $n$ nodes has exactly $\left\lceil \frac{n}{2} \right\rceil$ leaves, given that the heap is built in the following way:
Each new node is inserted via percolate up. This means that each new node must be created at the next available child. What I mean by this is that children ... |
I wonder if it is possible to build compilers for dynamic languages like Ruby to have similar and comparable performance to C/C++? From what I understand about compilers, take Ruby for instance, compiling Ruby code can't ever be efficient because the way Ruby handles reflection, features such as automatic type conversi... |
In a Whitted ray tracer, each ray-object intersection spawns a transmitted ray (if the object was translucent), a reflected ray and a shadow ray. The shadow ray contributes the direct lighting component.
But what happens if the shadow ray intersects a transparent object? Is the direct lighting component ignored? How wi... |
I'm curious. I've been working on this datatype in OCaml:
type 'a exptree =
| Epsilon
| Delta of 'a exptree * 'a exptree
| Omicron of 'a
| Iota of 'a exptree exptree
Which can be manipulated using explicitly typed recursive functions (a feature that has been added quite recently). Example:
let rec map : 'a 'b.... |
Over here, Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot is never proof. On second thought, I have to agree that this is a very useful approach that is even sometimes underused; a plo... |
The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time?
|
I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here.
Which are the relevant automated theorem provers? I found A Review of Theorem Provers
Is this still current?
Which ones are still very active, i.e. which are currently used... |
I have designed a classifier M which recognizes gestures and classifies it under any category always. A gesture is classified based on the hamming distance between the sample time series y and the training time series x. The result of the classifier are probabilistic values. There are 3 classes/categories with labels A... |
I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here.
Why is it that automated theorem provers, i.e. ACL2, and SMT solvers do not need human assistance while proof assistants, i.e. Isabelle and Coq, do?
Find the series' next q... |
A Fibonnaci Heap supports the following operations:
insert(key, data) : adds a new element to the data structure
find-min() : returns a pointer to the element with minimum key
delete-min() : removes the element with minimum key
delete(node) : deletes the element pointed to by node
decrease-key(node) : decreases the ke... |
I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here.
I keep reading about the Unification Algorithm.
What is it and why is so important to Inference Engines?
Why is it so important to Computer Science?
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What is a good beginner computer science book for a young adult, say, a 15 year old? I want to get started in CS, but have no idea where to start. I have limited experience in programming.
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Why cannot I find any information about spanning tree for DAG ? I must be wrong somewhere.
|
I often work with lexer/parsers, as opposed to a parser combinator and see people who never took a class in parsing, ask about parsing binary data. Typically the data is not only binary but also context sensitive. This basically leads to having only one type of token, a token for byte.
Can someone explain why parsing... |
Knapsack problems are easily solved by dynamic programming. Dynamic programming runs in polynomial time; that is why we do it, right?
I have read it is actually an NP-complete problem, though, which would mean that solving the problem in polynomial problem is probably impossible.
Where is my mistake?
|
In algorithm analysis you often have to solve recurrences. In addition to Master Theorem, substitution and iteration methods, there is one using characteristic polynomials.
Say I have concluded that a characteristic polynomial $x^2 - 2x + 2$ has imaginary roots, namely $x_1 = 1+i$ and $x_2 =1-i$. Then I cannot use
$\qq... |
I was explaining the famous deterministic linear-time selection algorithm (median of medians algorithm) to a friend.
The recursion in this algorithm (while being very simple) is quite sophisticated. There are two recursive calls, each with different parameters.
I was trying to find other examples of such interesting re... |
What would be the fastest way of doing this (from an algorithmic perspective, as well as a practical matter)?
I was thinking something along the following lines.
I could add to the end of an array and then use bubblesort as it has a best case (totally sorted array at start) that is close to this, and has linear running... |
I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found here.
This question concerns the computational power of type-2 min-heap automata, which were suggested by Raphael as a more nat... |
I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found here.
This question concerns the power of type-1 min-heap automata, which represent my initial idea for how these machines woul... |
There is this question I read somewhere but could not answer myself.
Assume I have an LR(1) Parsing table. Is there any way that just by looking at it and its items, can I deduce that it is also a table for LALR and SLR?
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It is known that each optimization/search problem has an equivalent decision problem. For example the shortest path problem
optimization/search version:
Given an undirected unweighted graph $G = (V, E)$ and two vertices $v,u\in V$, find a shortest path between $v$ and $u$.
decision version:
Given an undirected u... |
I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found here.
Two of my last questions seem to have been quickly dispatched; one completely, and the other mostly (I have edited it to ... |
According to Wikipedia:
Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained representation of that string.
What is the analogous informal rigorous definition of "useful information"? Why is "usefu... |
Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to think about different types of problems, and different fields use different formulation for this reason.
When I work wit... |
This a homework question from Udi Manber's book. Any hint would be nice :)
I must show that:
$n(\log_3(n))^5 = O(n^{1.2})$
I tried using Theorem 3.1 of book:
$f(n)^c = O(a^{f(n)})$ (for $c > 0$, $a > 1$)
Substituing:
$(\log_3(n))^5 = O(3^{\log_3(n)}) = O(n) $
but $n(\log_3(n))^5 = O(n\cdot n) = O(n^2) \ne O(n^{1.2}... |
I am slightly confused by some terminology I have encountered regarding the complexity of optimization problems. In an algorithms class, I had the large parsimony problem described as NP-complete. However, I am not exactly sure what the term NP-complete means in the context of an optimization problem. Does this just... |
I am trying to compare the performance of a classification result with Bayes classifier, K-NN, Piece wise component analysis (PCA). I have doubts regarding the following (please excuse my lack of programming skills since I am a biologist and not a programmer thus finding the Matlab documentation hard to follow).
In the... |
Consider a CSP model where changing the value of a particular variable is expensive. Is there any work where the objective function also considers the number of changes in the value of the variable during the search process?
An example: The expensive-to-change variable may be in the control of some other agent and ther... |
Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?
From what I can tell from wikipedia, the language needs to support recursion, or, seemingly, must be able to run without halting. Is this all there is to it?
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Codd's Algorithm converts an expression in tuple relational calculus to Relational Algebra.
Is there a standard implementation of the algorithm?
Is this algorithm used anywhere? (It seems that the industry only needs SQL and variants, I'm not sure about database theorists in academia.)
What's the complexity of the re... |
I am looking for an efficient algorithm that lets me process the minimax search tree for chess with alpha-beta pruning on a distributed architecture. The algorithms I have found (PVS, YBWC, DTS see below) are all quite old (1990 being the latest). I assume there have been many substantial advancements since then. What ... |
I ran into the following doubts on the complexity of Towers of Hanoi, on which I would like your comments.
Is it in NP?
Attempted answer: Suppose Peggy (prover) solves the problem & submits it to Victor (verifier). Victor can easily see that the final state of the solution is right (in linear time) but he'll have no... |
I wonder how to find the girth of a sparse undirected graph. By sparse I mean $|E|=O(|V|)$. By optimum I mean the lowest time complexity.
I thought about some modification on Tarjan's algorithm for undirected graphs, but I didn't find good results. Actually I thought that if I could find a 2-connected components in $O(... |
The Existential Theory of the Reals is in PSPACE, but I don't know whether it is PSPACE-Complete. If I believe that it is not the case, how could I prove it?
More generally, given a problem in some complexity class X, how can I show that it is not X-Complete? For example, X could be NP, PSPACE, EXPTIME.
|
Consider two 2D-Array $B_{ij} $ (the buy array) and $S_{ij}$ (the sell array) where each $i^{th}$ element is associated with an array of floating-point values and each of the floating point value, in turn, is associated with an array of integers.
For example
B = [
0001 => [ 32.5 => {10, 15, 20},
45.2 =>... |
Is it true that the set $\{ 0^{n^2} \mid n \in\mathbb{N} \}$ is not regular because it does not grow linearly?
Regular sets are called regular because if you have a regular set then you can always pump it up (pumping lemma) in regular intervals and get other things in the set. They string out at very linear intervals.... |
I know this is a simple question but can someone show me how
$(\lambda y. \lambda x. \lambda y.y) (\lambda x. \lambda y. y)$ reduces to $\lambda x. \lambda y. y$.
|
I have a test about the branch and bound algorithm. I understand theoretically how this algorithm works but I couldn't find examples that illustrates how this algorithm can be implemented practically.
I found some examples such as this one
but I'm still confused about it. I also looked for travelling salesman problem ... |
I am trying to figure out the simplest way to do this using a regular expression.
Three symbols a, b, c.
The sequence length is unlimited, i.e. *.
The symbol a must be somewhere in the sequence at least once, but can appear more than once.
The sequence may have only a.
More formally, $\{ w \in \{a,b,c\}^* ~|~ \#_a(... |
The main idea of k-Nearest-Neighbour takes into account the $k$ nearest points and decides the classification of the data by majority vote. If so, then it should not have problems in higher dimensional data because methods like locality sensitive hashing can efficiently find nearest neighbours.
In addition, feature sel... |
I have noticed that different data structures are used when we implement search algorithms. For example, we use queues to implement breadth first search, stacks to implement depth-first search and min-heaps to implement the A* algorithm. In these cases, we do not need to construct the search tree explicitly.
But I can ... |
I'm trying to use pumping lemma to prove that $L = \{(01)^m 2^m \mid m \ge0\}$ is not regular.
This is what I have so far: Assume $L$ is regular and let $p$ be the pumping length, so $w = (01)^p 2^p$. Consider any pumping decomposition $w = xyz$ such that $|y| >0$ and $|xy| \le p$.
I'm not sure what to do next.
Am I o... |
I have to write a grammar for Pascal, and there is just one thing that is causing problems.
Lets say we have operators (sorted by priority from low to high):
Postfix ^.
Prefix ^.
[ ], and ., (same priority and left associative).
The only terminal is id, which is any lowercase letter.
Now let's say that an expression... |
We learned about the class of regular languages $\mathrm{REG}$. It is characterised by any one concept among regular expressions, finite automata and left-linear grammars, so it is easy to show that a given language is regular.
How do I show the opposite, though? My TA has been adamant that in order to do so, we would ... |
According to Wikipedia, for any regular language $L$ there exist constants $\lambda_1,\ldots,\lambda_k$ and polynomials $p_1(x),\ldots,p_k(x)$ such that for every $n$ the number $s_L(n)$ of words of length $n$ in $L$ satisfies the equation
$\qquad \displaystyle s_L(n)=p_1(n)\lambda_1^n+\dots+p_k(n)\lambda_k^n$.
The la... |
Is there an algebraic characterization of the number of words of a given length in a regular language?
Wikipedia states a result somewhat imprecisely:
For any regular language $L$ there exist constants $\lambda_1,\,\ldots,\,\lambda_k$ and polynomials $p_1(x),\,\ldots,\,p_k(x)$
such that for every $n$ the number $s_L... |
Possible Duplicate:
Language of the values of an affine function
Let $C_n = \{x\mid x \text{ is a binary number that is a multiple of } n\}$. Show that for each $n$, the language $C_n$ is regular.
Just provide a generic recipe (i.e., a formal definition for arbitrary $n$).
|
Consider the following problem.
Given a set $S$ of integers, a function $f : \mathbb{Z} \to \mathbb{Z}$ and $k \in \mathbb{Z}$, decide wether there is $X \subseteq S$ such that $f\left(\sum_{x\in X}x\right)=k$.
Is this still considered a subset-sum problem?
For instance, given
$\qquad \displaystyle S=\{ −7, −3, −2, ... |
WalkSAT and GSAT are well-known and simple local search algorithms for solving the Boolean satisfiability problem. The pseudocode for the GSAT algorithm is copied from the question Implementing the GSAT algorithm - How to select which literal to flip? and presented below.
procedure GSAT(A,Max_Tries,Max_Flips)
A: is a... |
Assume we have a simple language that consists of the terms:
$\mathtt{true}$
$\mathtt{false}$
if $t_1,t_2,t_3$ are terms then so is $\mathtt{if}\: t_1 \:\mathtt{then}\: t_2 \:\mathtt{else}\: t_3$
Now assume the following logical evaluation rules:
$$ \begin{gather*}
\dfrac{}
{\mathtt{if}\: \mathtt{true} \:\mat... |
Let $G=(V,E)$ be some complete, weighted, undirected graph. We construct a second graph $G'=(V, E')$ by adding edges one by one from $E$ to $E'$. We add $\Theta(|V|)$ edges to $G'$ in total.
Every time we add one edge $(u,v)$ to $E'$, we consider the shortest distances between all pairs in $(V, E')$ and $(V, E' \cup \{... |
After reading several sources I'm still confused about user- and kernel-level threads.
In particular:
Threads can exist at both the user level and the kernel level
What is the difference between the user level and kernel level?
|
Consider a minimax tree for an adversarial search problem. For example, in this picture (alpha-beta pruning):
When marking the the tree with $[\min,\max]$ values bottom-up, we first traverse node $3$ and assign $B.\max = 3$. Then we traverse $12$ and $8$ in this order, it will make sure $B.max = 3$.
But why is $B.\min... |
I want to prove or disprove the existence of an algorithm which, given an array $A$ of integers, finds three indices $i, j$ and $k$ such that $i < j < k$ and $A[i] < A[j] < A[k]$ (or finds that there is no such triple) in linear time.
This is not a homework question; I saw it on a programming forum framed as “try to im... |
In other words, what advantages does Hybrid threading have over 1:1 (kernel only) and N:1 (user only) threading?
This is a follow-up to What is the difference between user-level threads and kernel-level threads?
|
This problem is taken from interviewstreet.com
We are given an array of integers $Y=\{y_1,...,y_n\}$ that represents $n$ line segments such that endpoints of segment $i$ are $(i, 0)$ and $(i, y_i)$. Imagine that from the top of each segment a horizontal ray is shot to the left, and this ray stops when it touches anothe... |
It seems as though modern speech recognition (e.g., through Android, iOS phones) make use of grammar or sentence structure. (e.g., it might have a tough time distinguishing between "grammar" and "grandma" but can distinguish between "I'm going to see grandma" and "I'm reading a book on english grammar". (yes, I just tr... |
I am currently working on a solution to a problem for which (after a bit of research) the use of a hill climbing, and more specificly a shotgun (or random-restart) hill climbing algorithmic idea seems to be the best fit, as I have no clue how the best start value can be found.
But there is not a lot of information abou... |
In a multicore processor, what happens to the contents of a core's cache (say L1) when a context switch occurs on that cache?
Is the behaviour dependent on the architecture or is it a general behaviour followed by all chip manufacturers?
|
I am working on an expression based language of ML genealogy, so it naturally needs type inference >:)
Now, I am trying to extend a constraint-based solution to the problem of inferring types, based on a simple implementation in EOPL (Friedman and Wand), but they elegantly side-step algebraic datatypes.
What I have so ... |
I have noticed in my short academic life that many published papers in our area sometimes do not have much rigor regarding statistics. This is not just an assumption; I have heard professors say the same.
For example, in CS disciplines I see papers being published claiming that methodology X has been observed to be ef... |
There are different queues of processes (in an operating system):
Job Queue: Each new process goes into the job queue. Processes in the job queue reside on mass storage and await the allocation of main memory.
Ready Queue: The set of all processes that are in main memory and are waiting for CPU time is kept in the read... |
I am trying to implement bidirectional search in a graph. I am using two breadth first searches from the start node and the goal node. The states that have been checked are stored in two hash tables (closed lists).
How can I get the solution (path from the start to the goal), when I find that a state that is checked by... |
I'm currently reading about machine learning and wondered how to apply it to playing Connect Four.
My current attempt is a simple multiclass classificator using a sigmoid function model and the one-vs-all method.
In my opinion, the input features have to be the state (disc of player 1, disc of player 2, empty) of the 7... |
Two things (this may be naive):
Does anyone believe there is a sub-exponential time algorithm for the Subset-sum problem? It seems obvious to me that you would have to look through all possible subsets to prove (the negation of) an existential statement. It seems obvious in the same way that if somebody asked you "Is ... |
I am confused about how taps are chosen for Linear Feedback Shift Registers.
I have a diagram which shows a LFSR with connection polynomial $C(X) = X^5 + X^2 + 1$. The five stages are labelled: $R4, R3, R2, R1$ and $R0$ and the taps come out of $R0$ and $R3$.
How are these taps decided? When I am given a connection pol... |
I was interested on evaluating a catalogue that students would be using to observe how is it being used probabilistically.
The catalogue works by choosing cells in a temporal sequence, so for example:
Student A has: ($t_1$,$Cell_3$),($t_2$,$Cell_4$)
Student B has: $(t_1,Cell_5),(t_2,Cell_3),(t_3,Cell_7)$.
Assume th... |
I once had a veteran in my course that created an algorithm that would suggest cooking recipes. At first, all sort of crazy recipes would come out. Then, she would train the cooking algorithm with real recipes and eventually it would suggest very good ones.
I believe she used something related to Bayes Theorem or Clus... |
On Alpha-Beta pruning, NegaScout claims that it can accelerate the process by setting [Alpha,Beta] to [Alpha,Alpha-1].
I do not understand the whole process of NegaScout.
How does it work? What is its recovery mechanism when its guessing failed?
|
In Michael Sipser's Theory of Computation on page 270 he writes:
P = the class of languages for which membership can be decided quickly.
NP = the class of languages for which membership can be verified quickly.
What is the difference between "decided" and "verified"?
|
For every computable function $f$ does there exist a problem that can be solved at best in $\Theta(f(n))$ time or is there a computable function $f$ such that every problem that can be solved in $O(f(n))$ can also be solved in $o(f(n))$ time?
This question popped into my head yesterday. I've been thinking about it for ... |
Suppose I am given a finite set of points $p_1,p_2,..p_n$ in the plane, and asked to draw a twice-differentiable curve $C(P)$ through the $p_i$'s, such that its perimeter is as small as possible. Assuming $p_i=(x_i,y_i)$ and $x_i<x_{i+1}$, I can formalize this problem as:
Problem 1 (edited in response to Suresh's com... |
I want to establish that this is part of my homework for a course I am currently taking. I am looking for some assistance in proceeding, NOT AN ANSWER.
This is the question in question:
A 5-pointed-star in an undirected graph is a 5-clique. Show that
5-POINTED-STAR $\in P$, where 5-POINTED-STAR = $\{ <G>$ $: G$ con... |
I am interested in calculating the $n$'th power of a $n\times n$ matrix $A$. Suppose we have an algorithm for matrix multiplication which runs in $\mathcal{O}(M(n))$ time. Then, one can easily calculate $A^n$ in $\mathcal{O}(M(n)\log(n))$ time. Is it possible to solve this problem in lesser time complexity?
Matrix entr... |
I am wondering if there are any experiments that show the existence or the non-existence of a correlation between usage of a dynamic language (such as Python, Ruby, or even languages that run on the Java platform such as Groovy, Clojure) over a static language (such as C/C++), and the difference in the productivity.
|
I am implementing a set of path finding algorithms such as Dijkstra's, Depth First, etc.
At first I used a couple of self made graphs, but now I'd like to take the challenge a bit further and thus I'm looking for either
graphs used in benchmarks;
graphs of real world cities (or a way to download that kind of info off ... |
This question might seems vague but heres the context:
When we are focusing on HCI we would most likely be interested on knowing first how the user usually deals with a certain object. We then try to see how our system could take away one of the tasks he would do himself and try to do it itself.
The object of my inte... |
My question goes to those who are concerned with computational biology algorithmics. I'm going to take a course on bioinformatics this fall; the problem, however, is that I have too little background in biology and chemistry to feel prepared for that cycle of lections (I was rather weak at these subjects at school).
Co... |
I have developed the following pseudocode for the sum of pairs problem:
Given an array $A$ of integers and an integer $b$, return YES if there are positions $i,j$ in $A$ with $A[i] + A[j] = b$, NO otherwise.
Now I should state a loop invariant that shows that my algorithm is correct. Can someone give me a hint of a v... |
Let me start off by noting this is a homework problem, please provide only advice and related observations, NO DIRECT ANSWERS please. With that said, here is the problem I am looking at:
Let HALF-CLIQUE = { $\langle G \rangle$ | $G$ is an undirected graph having a complete
subgraph with at least $n/2$ nodes, where ... |
In the discussion around this question, Gilles mentions correctly that any correctness proof of an algorithm that uses arrays has to prove that there are no out-of-bounds array accesses; depending on the runtime model, this would cause a runtime error or access to non-array elements.
One common technique to perform suc... |
I would like to write a simple program that accepts a set of windows (width+height) and the screen resolution and outputs an arrangement of those windows on the screen such that the windows take the most space. Therefore it is possible to resize a window, while maintaining output size >= initial size and the aspect ra... |
Having a set $A$ of $n$ elements, let's say I want to calculate a function $f(A)$ that is sensitive to all parts of the input, i.e. depends on very member of $A$ (i.e. it is possible to change any member of $A$ to something else to obtain a new input $A'$ s.t. value of $f$ on $A$ and $A'$ are different).
For example, $... |
I have the following algorithmic problem:
Determine the space Turing complexity of recognizing DNA strings that are Watson-Crick palindromes.
Watson-Crick palindromes are strings whose reversed complement is the original string. The complement is defined letter-wise, inspired by DNA: A is the complement of T and C i... |
I am revising for a computer security course and I am stuck on one of the past questions. Here is it:
Alice ($A$) wants to send a short message $M$ to Bob ($B$) using a shared secret $S_{ab}$ to authenticate that the message has come from her. She proposes to send a single message with two pieces:
$$ A \to B: \quad ... |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem instanc... |
I don't quite understand why the rotation in the splay tree data structure is taking into account not only the parent of the rating node, but also the grandparent (zig-zag and zig-zig operation). Why would the following not work:
As we insert, for instance, a new node to the tree, we check whether we insert into the le... |
Suppose we have a set $S = \{ a_1,a_2,a_3,\ldots , a_N \}$ of $N$ coders.
Each Coders has rating $R_i$ and the number of gold medals $E_i$, they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders, they developed the following strategy:
They first a... |
Recently I found in a paper [1] a special symmetric version of SAT called the 2/2/4-SAT. But there are many $\text{NP}$-complete variants out there, for example: MONOTONE NAE-3SAT, MONOTONE 1-IN-3-SAT, ...
Some other variants are tractable: $2$-$\text{SAT}$, Planar-NAE-$\text{SAT}$, ...
Are there survey papers (or web ... |
Let's say that we have a large collection of tasks $\tau_1, \tau_2, ..., \tau_n$ and a collection of identical (in terms of performance) processors $\rho_1, \rho_2, ..., \rho_m$ which operate completely in parallel. For scenarios of interest, we may assume $m \leq n$. Each $\tau_i$ takes some amount of time/cycles to c... |
Often I see a sentence like this while reading texts on Computational Complexity:
"For this special case of $\text{TSP}$" or
"This is a special case of $\text{SAT}$" or
"$k$-$\text{PARTITION}$ is the following special case of $\text{BIN PACKING}$" or
"$\text{SUBSET SUM}$ is a special case of $\text{KNAPSACK}$" ad nause... |
I am taking a complexity course and I am having trouble with coming up with reductions between NPC problems. How can I find reductions between problems? Is there a general trick that I can use? How should I approach a problem that asks me to prove a problem is NPC?
|
In many textbooks NP problems are defined as:
Set of all decision problems solvable by non deterministic algorithms in polynomial time
I couldn't understand the part "solvable by non deterministic algorithms". Could anyone please explain that?
|
I need to cover these topics in Role Mining. If anyone knows good site which well summarizes the topics and concepts are well explained please help out.
Basic role mining problem
• Delta-approx RMP
• Min-noise RMP
• Nature of the RMP problems
• Mapping RMP to database tiling problem
• Minimum tiling problem
• Mapping m... |
Given an integer $n$ and set of triplets of distinct integers
$$S \subseteq \{(i, j, k) \mid 1\le i,j,k \le n, i \neq j, j \neq k, i \neq k\},$$
find an algorithm which either finds a permutation $\pi$ of the set $\{1, 2, \dots, n\}$ such that
$$(i,j,k) \in S \implies (\pi(j)<\pi(i)<\pi(k)) ~\lor~ (\pi(i)<\pi(k)<\pi(j)... |
I am writing a Program, solving the Chinese Postman Problem (also known as route inspection problem) in an undirected draph and currently facing the problem to find the best additional edges to connect the nodes with odd degree, so I can compute an Eulerian circuit.
There might be (considering the size of the graph tha... |
I understand that a Church numeral $c_n$ looks like $\lambda s. \lambda z. s$ (... n times ...) $s\;z$. This means nothing more than "the function $s$ applied $n$ times to the function $z$".
A possible definition of the $\mathtt{times}$ function is the following: $\mathtt{times} = \lambda m. \lambda n. \lambda s. m \; ... |
(this is related to my other question, see here)
Imagine a screen, with 3 windows on it:
I'd like to find an efficient data structure to represent this, while supporting these actions:
return a list of coordinates where a given window can be positioned without overlapping with others
for the above example, if we wa... |
For the following jobs:
The average wait time would be using a FCFS algorithm:
(6-6)+(7-2)+(11-5)+(17-5)+(14-1) -> 0+5+6+10+13 -> 34/5 = 7 (6.8)
What would the average turnaround time be?
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