task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-nppc-clique-l4-s6 | construct | nppc_clique | graph_clique | graph_theory | competition | 4 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 283 edges:
[[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [1, 3], [1, 4], [1, 5], [1, 7], [1, 9], [1, 15]... | {"num_nodes": 30, "k": 15, "edges": [[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [1, 3], [1, 4], [1, 5], [1, 7], [1, 9], [1, 15], [1, 16], [1, 22], [1, 24],... | null | null | null | {"clique": [0, 2, 3, 6, 7, 8, 9, 10, 15, 17, 21, 25, 26, 27, 28]} | 1 |
construct-nppc-clique-l4-s7 | construct | nppc_clique | graph_clique | graph_theory | competition | 4 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 263 edges:
[[0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 23], [0, 27], [0, 28], [0, 29], [1, 3], [1, 4], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1,... | {"num_nodes": 30, "k": 15, "edges": [[0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 23], [0, 27], [0, 28], [0, 29], [1, 3], [1, 4], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 23], [1, 26], [1, ... | null | null | null | {"clique": [0, 3, 4, 6, 8, 9, 10, 11, 12, 17, 19, 20, 23, 27, 28]} | 1 |
construct-nppc-clique-l4-s8 | construct | nppc_clique | graph_clique | graph_theory | competition | 4 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 275 edges:
[[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 25], [0, 26], [0, 28], [0, 29], [1, 2], [1, 3], [1, 4], [1, 5], [1, 9], [1, 10], [1, 12... | {"num_nodes": 30, "k": 15, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 25], [0, 26], [0, 28], [0, 29], [1, 2], [1, 3], [1, 4], [1, 5], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15]... | null | null | null | {"clique": [0, 1, 3, 4, 9, 13, 14, 16, 17, 18, 19, 20, 21, 22, 25]} | 1 |
construct-nppc-clique-l4-s9 | construct | nppc_clique | graph_clique | graph_theory | competition | 4 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 289 edges:
[[0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [0, 29], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 11], [1, 14]... | {"num_nodes": 30, "k": 15, "edges": [[0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [0, 29], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 11], [1, 14], [1, 16], [1, 17], [1, 20],... | null | null | null | {"clique": [0, 4, 5, 6, 7, 12, 13, 16, 17, 19, 21, 23, 26, 27, 29]} | 1 |
construct-nppc-clique-l5-s0 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 470 edges:
[[0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [0, 17], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 28], [0, 29], [0, 30], [0, 32], [0, 34], [0, 36], [0, 37], [0, 38], [1, 3], [1, 5], [1, 6], [1, 10], [1, 11], [1, 12], [1, 13], [1, 15], ... | {"num_nodes": 40, "k": 20, "edges": [[0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [0, 17], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 28], [0, 29], [0, 30], [0, 32], [0, 34], [0, 36], [0, 37], [0, 38], [1, 3], [1, 5], [1, 6], [1, 10], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [... | null | null | null | {"clique": [1, 3, 5, 6, 11, 13, 15, 16, 17, 18, 22, 23, 25, 27, 29, 31, 33, 35, 37, 38]} | 1 |
construct-nppc-clique-l5-s1 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 483 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], ... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 3], [1... | null | null | null | {"clique": [0, 2, 3, 4, 5, 8, 10, 15, 16, 17, 18, 20, 25, 26, 28, 34, 35, 37, 38, 39]} | 1 |
construct-nppc-clique-l5-s2 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 485 edges:
[[0, 1], [0, 2], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 2], [1, 3], [1, ... | null | null | null | {"clique": [0, 2, 6, 7, 9, 11, 12, 17, 18, 21, 23, 24, 27, 29, 32, 35, 36, 37, 38, 39]} | 1 |
construct-nppc-clique-l5-s3 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 480 edges:
[[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 36], [0, 37], [0, 38], [0, 39], [1, 2], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 36], [0, 37], [0, 38], [0, 39], [1, 2], [1, 3], [1, 4], [1, 5], [1, 8... | null | null | null | {"clique": [0, 3, 5, 6, 8, 10, 13, 14, 16, 19, 21, 23, 24, 28, 29, 30, 31, 36, 37, 39]} | 1 |
construct-nppc-clique-l5-s4 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 457 edges:
[[0, 5], [0, 9], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 22], [0, 23], [0, 26], [0, 27], [0, 28], [0, 29], [0, 33], [0, 38], [0, 39], [1, 3], [1, 4], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 5], [0, 9], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 22], [0, 23], [0, 26], [0, 27], [0, 28], [0, 29], [0, 33], [0, 38], [0, 39], [1, 3], [1, 4], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 24], [1, 25], [1, 26], [1... | null | null | null | {"clique": [3, 6, 7, 8, 10, 12, 13, 15, 18, 22, 24, 27, 28, 30, 32, 33, 34, 35, 37, 38]} | 1 |
construct-nppc-clique-l5-s5 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 495 edges:
[[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 27], [0, 29], [0, 30], [0, 32], [0, 33], [0, 35], [0, 36], [0, 37], [0... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 27], [0, 29], [0, 30], [0, 32], [0, 33], [0, 35], [0, 36], [0, 37], [0, 39], [1, 2], [1, 3], [1, 4... | null | null | null | {"clique": [0, 1, 2, 4, 6, 7, 9, 10, 11, 14, 16, 17, 20, 22, 26, 33, 35, 36, 37, 39]} | 1 |
construct-nppc-clique-l5-s6 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 480 edges:
[[0, 5], [0, 7], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 19], [0, 26], [0, 27], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 38], [0, 39], [1, 2], [1, 3], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 17], [1, 18], [1, 19], [1, 20], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 5], [0, 7], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 19], [0, 26], [0, 27], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 38], [0, 39], [1, 2], [1, 3], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1... | null | null | null | {"clique": [1, 6, 8, 9, 12, 17, 18, 20, 21, 24, 25, 26, 30, 32, 33, 34, 35, 36, 37, 39]} | 1 |
construct-nppc-clique-l5-s7 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 479 edges:
[[0, 1], [0, 2], [0, 7], [0, 9], [0, 16], [0, 20], [0, 24], [0, 26], [0, 28], [0, 29], [0, 36], [0, 38], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [1, 2... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 7], [0, 9], [0, 16], [0, 20], [0, 24], [0, 26], [0, 28], [0, 29], [0, 36], [0, 38], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [1, 24], [1, 25], [1, 27], [1, 28... | null | null | null | {"clique": [1, 2, 4, 6, 8, 9, 10, 11, 16, 18, 22, 28, 29, 30, 31, 32, 33, 34, 36, 38]} | 1 |
construct-nppc-clique-l5-s8 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 470 edges:
[[0, 2], [0, 5], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39... | {"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 5], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 3], [1, 4], [1, 5], [... | null | null | null | {"clique": [0, 2, 12, 13, 14, 15, 16, 17, 18, 22, 24, 25, 26, 30, 31, 32, 33, 36, 38, 39]} | 1 |
construct-nppc-clique-l5-s9 | construct | nppc_clique | graph_clique | graph_theory | competition | 5 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 482 edges:
[[0, 3], [0, 4], [0, 5], [0, 12], [0, 16], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 30], [0, 33], [0, 34], [0, 36], [0, 37], [0, 39], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 19], [1, ... | {"num_nodes": 40, "k": 20, "edges": [[0, 3], [0, 4], [0, 5], [0, 12], [0, 16], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 30], [0, 33], [0, 34], [0, 36], [0, 37], [0, 39], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 19], [1, 20], [1, 21], [1, 23], [1, 2... | null | null | null | {"clique": [2, 3, 6, 7, 8, 9, 10, 14, 15, 17, 20, 22, 23, 24, 26, 29, 30, 31, 33, 36]} | 1 |
construct-nppc-clique-l6-s0 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2567 edges:
[[0, 1], [0, 3], [0, 5], [0, 6], [0, 7], [0, 10], [0, 12], [0, 14], [0, 18], [0, 20], [0, 21], [0, 23], [0, 26], [0, 28], [0, 30], [0, 31], [0, 39], [0, 40], [0, 43], [0, 44], [0, 48], [0, 49], [0, 50], [0, 52], [0, 53], [0, 56], [0, 58], [0, 62], [0, 63... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 3], [0, 5], [0, 6], [0, 7], [0, 10], [0, 12], [0, 14], [0, 18], [0, 20], [0, 21], [0, 23], [0, 26], [0, 28], [0, 30], [0, 31], [0, 39], [0, 40], [0, 43], [0, 44], [0, 48], [0, 49], [0, 50], [0, 52], [0, 53], [0, 56], [0, 58], [0, 62], [0, 63], [0, 66], [0, 68], [0, 69],... | null | null | null | {"clique": [5, 17, 27, 35, 40, 43, 46, 47, 48, 50, 51, 52, 55, 56, 69, 70, 74, 79, 87, 91]} | 1 |
construct-nppc-clique-l6-s1 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2565 edges:
[[0, 1], [0, 2], [0, 6], [0, 17], [0, 18], [0, 20], [0, 24], [0, 25], [0, 27], [0, 29], [0, 30], [0, 32], [0, 35], [0, 37], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 48], [0, 49], [0, 53], [0, 54], [0, 55], [0, 56], [0, 57], [0, 59], [0, 61], [0, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 6], [0, 17], [0, 18], [0, 20], [0, 24], [0, 25], [0, 27], [0, 29], [0, 30], [0, 32], [0, 35], [0, 37], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 48], [0, 49], [0, 53], [0, 54], [0, 55], [0, 56], [0, 57], [0, 59], [0, 61], [0, 65], [0, 68], [0, 70], [0, 71... | null | null | null | {"clique": [2, 10, 13, 20, 26, 27, 29, 39, 43, 46, 48, 50, 51, 56, 59, 79, 80, 84, 91, 98]} | 1 |
construct-nppc-clique-l6-s2 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2555 edges:
[[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [0, 16], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 36], [0, 38],... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [0, 16], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 36], [0, 38], [0, 40], [0, 42], [0, 44], [... | null | null | null | {"clique": [1, 5, 7, 12, 26, 29, 35, 36, 38, 47, 56, 63, 65, 77, 80, 81, 86, 91, 97, 98]} | 1 |
construct-nppc-clique-l6-s3 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2580 edges:
[[0, 2], [0, 4], [0, 5], [0, 8], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 22], [0, 23], [0, 24], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 33], [0, 35], [0, 38], [0, 40], [0, 41], [0, 44], [0, 46], [0, 4... | {"num_nodes": 100, "k": 20, "edges": [[0, 2], [0, 4], [0, 5], [0, 8], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 22], [0, 23], [0, 24], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 33], [0, 35], [0, 38], [0, 40], [0, 41], [0, 44], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50]... | null | null | null | {"clique": [10, 15, 26, 28, 30, 31, 51, 60, 65, 68, 69, 74, 76, 80, 81, 84, 85, 90, 91, 92]} | 1 |
construct-nppc-clique-l6-s4 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2552 edges:
[[0, 1], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 19], [0, 21], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 38], [0, 40], [0, 41], [0, 42], [0, 44], [0, 45], [0, 46], [0, 47]... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 19], [0, 21], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 38], [0, 40], [0, 41], [0, 42], [0, 44], [0, 45], [0, 46], [0, 47], [0, 51], [0, 54], [0, 55], ... | null | null | null | {"clique": [0, 4, 5, 6, 7, 11, 15, 19, 21, 28, 30, 31, 38, 41, 46, 65, 77, 78, 85, 98]} | 1 |
construct-nppc-clique-l6-s5 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2562 edges:
[[0, 5], [0, 6], [0, 7], [0, 11], [0, 15], [0, 16], [0, 17], [0, 18], [0, 25], [0, 29], [0, 30], [0, 33], [0, 37], [0, 38], [0, 39], [0, 42], [0, 44], [0, 46], [0, 47], [0, 53], [0, 54], [0, 56], [0, 58], [0, 59], [0, 62], [0, 63], [0, 64], [0, 65], [0, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 5], [0, 6], [0, 7], [0, 11], [0, 15], [0, 16], [0, 17], [0, 18], [0, 25], [0, 29], [0, 30], [0, 33], [0, 37], [0, 38], [0, 39], [0, 42], [0, 44], [0, 46], [0, 47], [0, 53], [0, 54], [0, 56], [0, 58], [0, 59], [0, 62], [0, 63], [0, 64], [0, 65], [0, 68], [0, 69], [0, 75], [0, 76... | null | null | null | {"clique": [7, 8, 10, 19, 27, 28, 36, 42, 43, 45, 50, 52, 54, 61, 62, 68, 70, 73, 86, 87]} | 1 |
construct-nppc-clique-l6-s6 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2618 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 12], [0, 13], [0, 14], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 25], [0, 26], [0, 28], [0, 31], [0, 34], [0, 36], [0, 37], [0, 39], [0, 42], [0, 44], [0, 46], [0, 49], ... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 12], [0, 13], [0, 14], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 25], [0, 26], [0, 28], [0, 31], [0, 34], [0, 36], [0, 37], [0, 39], [0, 42], [0, 44], [0, 46], [0, 49], [0, 50], [0, 51], [0, 52], [0... | null | null | null | {"clique": [0, 1, 3, 6, 12, 13, 14, 16, 19, 21, 25, 28, 36, 37, 49, 50, 66, 71, 86, 92]} | 1 |
construct-nppc-clique-l6-s7 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2600 edges:
[[0, 4], [0, 5], [0, 6], [0, 9], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 18], [0, 20], [0, 25], [0, 28], [0, 32], [0, 33], [0, 34], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 47], [0, 49], [0, 52], [0, 53], [0, 54], [0, 55], [0, 56], [0, 5... | {"num_nodes": 100, "k": 20, "edges": [[0, 4], [0, 5], [0, 6], [0, 9], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 18], [0, 20], [0, 25], [0, 28], [0, 32], [0, 33], [0, 34], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 47], [0, 49], [0, 52], [0, 53], [0, 54], [0, 55], [0, 56], [0, 57], [0, 59], [0, 61], [0, 62]... | null | null | null | {"clique": [11, 13, 20, 23, 36, 38, 41, 42, 52, 53, 57, 60, 62, 65, 74, 80, 85, 90, 96, 98]} | 1 |
construct-nppc-clique-l6-s8 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2552 edges:
[[0, 1], [0, 2], [0, 4], [0, 5], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 18], [0, 22], [0, 23], [0, 26], [0, 30], [0, 32], [0, 33], [0, 36], [0, 41], [0, 43], [0, 45], [0, 46], [0, 47], [0, 50], [0, 51], [0, 52], [0, 54], [0, 55], [0, 56], [0, 5... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 18], [0, 22], [0, 23], [0, 26], [0, 30], [0, 32], [0, 33], [0, 36], [0, 41], [0, 43], [0, 45], [0, 46], [0, 47], [0, 50], [0, 51], [0, 52], [0, 54], [0, 55], [0, 56], [0, 57], [0, 58], [0, 60], [0, 61]... | null | null | null | {"clique": [21, 24, 28, 29, 30, 34, 40, 43, 63, 70, 76, 77, 82, 86, 89, 93, 94, 95, 96, 99]} | 1 |
construct-nppc-clique-l6-s9 | construct | nppc_clique | graph_clique | graph_theory | competition | 6 | NPPC/clique | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 2542 edges:
[[0, 3], [0, 7], [0, 12], [0, 15], [0, 16], [0, 18], [0, 19], [0, 22], [0, 27], [0, 29], [0, 30], [0, 31], [0, 33], [0, 34], [0, 36], [0, 37], [0, 39], [0, 43], [0, 47], [0, 48], [0, 50], [0, 51], [0, 54], [0, 55], [0, 56], [0, 58], [0, 65], [0, 66], [0,... | {"num_nodes": 100, "k": 20, "edges": [[0, 3], [0, 7], [0, 12], [0, 15], [0, 16], [0, 18], [0, 19], [0, 22], [0, 27], [0, 29], [0, 30], [0, 31], [0, 33], [0, 34], [0, 36], [0, 37], [0, 39], [0, 43], [0, 47], [0, 48], [0, 50], [0, 51], [0, 54], [0, 55], [0, 56], [0, 58], [0, 65], [0, 66], [0, 68], [0, 69], [0, 71], [0, 7... | null | null | null | {"clique": [1, 9, 14, 23, 24, 32, 35, 37, 43, 49, 63, 64, 67, 71, 74, 77, 81, 83, 93, 94]} | 1 |
construct-nppc-dominating-set-l1-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 19 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 9], [2, 7], [3, 6], [3, 8], [3, 9], [4, 6], [4, 8], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or ... | {"num_nodes": 10, "k": 5, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 9], [2, 7], [3, 6], [3, 8], [3, 9], [4, 6], [4, 8], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [0, 3, 4, 6, 7]} | 1 |
construct-nppc-dominating-set-l1-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 20 edges:
[[0, 2], [0, 3], [0, 5], [1, 4], [1, 6], [1, 9], [2, 3], [2, 5], [2, 6], [2, 7], [2, 9], [3, 5], [3, 7], [3, 9], [4, 6], [5, 6], [5, 7], [5, 9], [6, 8], [8, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is ... | {"num_nodes": 10, "k": 5, "edges": [[0, 2], [0, 3], [0, 5], [1, 4], [1, 6], [1, 9], [2, 3], [2, 5], [2, 6], [2, 7], [2, 9], [3, 5], [3, 7], [3, 9], [4, 6], [5, 6], [5, 7], [5, 9], [6, 8], [8, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [2, 3, 4, 6, 9]} | 1 |
construct-nppc-dominating-set-l1-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 17 edges:
[[0, 3], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 7], [1, 8], [2, 3], [3, 7], [3, 8], [3, 9], [4, 5], [4, 7], [4, 9], [5, 9], [6, 8]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a ve... | {"num_nodes": 10, "k": 5, "edges": [[0, 3], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 7], [1, 8], [2, 3], [3, 7], [3, 8], [3, 9], [4, 5], [4, 7], [4, 9], [5, 9], [6, 8]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [1, 3, 5, 6, 7]} | 1 |
construct-nppc-dominating-set-l1-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 15 edges:
[[0, 1], [0, 5], [0, 9], [1, 4], [1, 5], [1, 7], [1, 8], [2, 3], [2, 4], [2, 9], [3, 4], [3, 6], [5, 6], [5, 8], [7, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
Answ... | {"num_nodes": 10, "k": 5, "edges": [[0, 1], [0, 5], [0, 9], [1, 4], [1, 5], [1, 7], [1, 8], [2, 3], [2, 4], [2, 9], [3, 4], [3, 6], [5, 6], [5, 8], [7, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [3, 4, 5, 7, 8]} | 1 |
construct-nppc-dominating-set-l1-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 15 edges:
[[0, 5], [0, 6], [0, 7], [1, 3], [1, 4], [1, 8], [2, 4], [2, 6], [2, 8], [3, 8], [3, 9], [4, 6], [5, 7], [5, 9], [8, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
Answ... | {"num_nodes": 10, "k": 5, "edges": [[0, 5], [0, 6], [0, 7], [1, 3], [1, 4], [1, 8], [2, 4], [2, 6], [2, 8], [3, 8], [3, 9], [4, 6], [5, 7], [5, 9], [8, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [4, 6, 7, 8, 9]} | 1 |
construct-nppc-dominating-set-l1-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 11 edges:
[[0, 2], [0, 7], [0, 8], [0, 9], [1, 2], [1, 6], [3, 5], [3, 7], [3, 9], [4, 6], [4, 8]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
Answer format: {"dominating_set": [v... | {"num_nodes": 10, "k": 5, "edges": [[0, 2], [0, 7], [0, 8], [0, 9], [1, 2], [1, 6], [3, 5], [3, 7], [3, 9], [4, 6], [4, 8]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [2, 3, 6, 8, 9]} | 1 |
construct-nppc-dominating-set-l1-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 17 edges:
[[0, 6], [1, 2], [1, 4], [1, 5], [2, 4], [2, 8], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [4, 6], [5, 6], [5, 8], [6, 7], [7, 9], [8, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a ve... | {"num_nodes": 10, "k": 5, "edges": [[0, 6], [1, 2], [1, 4], [1, 5], [2, 4], [2, 8], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [4, 6], [5, 6], [5, 8], [6, 7], [7, 9], [8, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [1, 3, 6, 8, 9]} | 1 |
construct-nppc-dominating-set-l1-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 16 edges:
[[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [1, 4], [1, 8], [2, 3], [2, 5], [3, 4], [3, 5], [3, 6], [4, 7], [5, 8], [6, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of ... | {"num_nodes": 10, "k": 5, "edges": [[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [1, 4], [1, 8], [2, 3], [2, 5], [3, 4], [3, 5], [3, 6], [4, 7], [5, 8], [6, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [0, 1, 5, 6, 7]} | 1 |
construct-nppc-dominating-set-l1-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 15 edges:
[[0, 6], [0, 8], [0, 9], [1, 2], [1, 3], [1, 7], [2, 3], [2, 6], [2, 8], [3, 6], [3, 8], [3, 9], [4, 6], [6, 7], [7, 8]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
Answ... | {"num_nodes": 10, "k": 5, "edges": [[0, 6], [0, 8], [0, 9], [1, 2], [1, 3], [1, 7], [2, 3], [2, 6], [2, 8], [3, 6], [3, 8], [3, 9], [4, 6], [6, 7], [7, 8]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [0, 3, 4, 5, 7]} | 1 |
construct-nppc-dominating-set-l1-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 1 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 10 vertices labelled 0..9 and 17 edges:
[[0, 2], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 8], [2, 3], [2, 7], [3, 5], [3, 6], [3, 7], [4, 5], [4, 7], [4, 8], [7, 8], [8, 9]]
Find a dominating set of size at most 5: a set D of distinct vertices such that every vertex is in D or adjacent to a ve... | {"num_nodes": 10, "k": 5, "edges": [[0, 2], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 8], [2, 3], [2, 7], [3, 5], [3, 6], [3, 7], [4, 5], [4, 7], [4, 8], [7, 8], [8, 9]], "family": "nppc_dominating_set", "subset": "construct"} | null | null | null | {"dominating_set": [2, 3, 5, 8, 9]} | 1 |
construct-nppc-dominating-set-l2-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 150 edges:
[[0, 3], [0, 5], [0, 6], [0, 11], [0, 15], [0, 17], [0, 19], [0, 21], [0, 23], [0, 26], [1, 12], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [1, 23], [2, 3], [2, 6], [2, 7], [2, 9], [2, 15], [2, 16], [2, 25], [2, 26], [2, 28], [2, 29], [3, 7], [3... | {"num_nodes": 30, "k": 15, "edges": [[0, 3], [0, 5], [0, 6], [0, 11], [0, 15], [0, 17], [0, 19], [0, 21], [0, 23], [0, 26], [1, 12], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [1, 23], [2, 3], [2, 6], [2, 7], [2, 9], [2, 15], [2, 16], [2, 25], [2, 26], [2, 28], [2, 29], [3, 7], [3, 12], [3, 17], [3, 20], [3,... | null | null | null | {"dominating_set": [6, 7, 9, 11, 12, 13, 15, 16, 19, 20, 21, 23, 24, 25, 28]} | 1 |
construct-nppc-dominating-set-l2-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 133 edges:
[[0, 2], [0, 4], [0, 5], [0, 6], [0, 13], [0, 17], [0, 20], [0, 22], [0, 23], [0, 24], [0, 25], [1, 4], [1, 8], [1, 10], [1, 12], [1, 13], [1, 19], [1, 23], [1, 28], [1, 29], [2, 11], [2, 23], [2, 25], [2, 27], [2, 29], [3, 4], [3, 6], [3, 10], [3, 12], [3... | {"num_nodes": 30, "k": 15, "edges": [[0, 2], [0, 4], [0, 5], [0, 6], [0, 13], [0, 17], [0, 20], [0, 22], [0, 23], [0, 24], [0, 25], [1, 4], [1, 8], [1, 10], [1, 12], [1, 13], [1, 19], [1, 23], [1, 28], [1, 29], [2, 11], [2, 23], [2, 25], [2, 27], [2, 29], [3, 4], [3, 6], [3, 10], [3, 12], [3, 17], [3, 21], [3, 24], [3,... | null | null | null | {"dominating_set": [0, 2, 5, 7, 8, 9, 12, 13, 17, 19, 22, 23, 26, 28, 29]} | 1 |
construct-nppc-dominating-set-l2-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 148 edges:
[[0, 6], [0, 7], [0, 8], [0, 13], [0, 14], [0, 15], [0, 16], [0, 18], [0, 20], [0, 24], [0, 25], [0, 27], [0, 29], [1, 5], [1, 6], [1, 9], [1, 19], [1, 24], [1, 27], [1, 29], [2, 3], [2, 4], [2, 8], [2, 9], [2, 10], [2, 16], [2, 17], [2, 18], [2, 23], [2, ... | {"num_nodes": 30, "k": 15, "edges": [[0, 6], [0, 7], [0, 8], [0, 13], [0, 14], [0, 15], [0, 16], [0, 18], [0, 20], [0, 24], [0, 25], [0, 27], [0, 29], [1, 5], [1, 6], [1, 9], [1, 19], [1, 24], [1, 27], [1, 29], [2, 3], [2, 4], [2, 8], [2, 9], [2, 10], [2, 16], [2, 17], [2, 18], [2, 23], [2, 24], [2, 25], [2, 26], [2, 2... | null | null | null | {"dominating_set": [3, 6, 7, 10, 13, 14, 15, 19, 21, 22, 23, 24, 26, 28, 29]} | 1 |
construct-nppc-dominating-set-l2-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 146 edges:
[[0, 3], [0, 4], [0, 5], [0, 8], [0, 13], [0, 14], [0, 19], [0, 21], [0, 23], [0, 24], [0, 25], [0, 28], [0, 29], [1, 5], [1, 8], [1, 16], [1, 17], [1, 22], [1, 26], [1, 28], [2, 3], [2, 6], [2, 9], [2, 10], [2, 11], [2, 14], [2, 18], [2, 19], [2, 21], [2,... | {"num_nodes": 30, "k": 15, "edges": [[0, 3], [0, 4], [0, 5], [0, 8], [0, 13], [0, 14], [0, 19], [0, 21], [0, 23], [0, 24], [0, 25], [0, 28], [0, 29], [1, 5], [1, 8], [1, 16], [1, 17], [1, 22], [1, 26], [1, 28], [2, 3], [2, 6], [2, 9], [2, 10], [2, 11], [2, 14], [2, 18], [2, 19], [2, 21], [2, 22], [2, 24], [2, 28], [3, ... | null | null | null | {"dominating_set": [0, 2, 3, 4, 6, 7, 8, 11, 12, 14, 17, 23, 24, 25, 28]} | 1 |
construct-nppc-dominating-set-l2-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 159 edges:
[[0, 3], [0, 4], [0, 7], [0, 8], [0, 12], [0, 16], [0, 17], [0, 18], [0, 21], [0, 22], [0, 25], [0, 28], [1, 4], [1, 5], [1, 7], [1, 9], [1, 14], [1, 15], [1, 26], [1, 27], [1, 28], [1, 29], [2, 3], [2, 6], [2, 10], [2, 13], [2, 18], [2, 19], [2, 21], [2, ... | {"num_nodes": 30, "k": 15, "edges": [[0, 3], [0, 4], [0, 7], [0, 8], [0, 12], [0, 16], [0, 17], [0, 18], [0, 21], [0, 22], [0, 25], [0, 28], [1, 4], [1, 5], [1, 7], [1, 9], [1, 14], [1, 15], [1, 26], [1, 27], [1, 28], [1, 29], [2, 3], [2, 6], [2, 10], [2, 13], [2, 18], [2, 19], [2, 21], [2, 23], [2, 24], [2, 28], [2, 2... | null | null | null | {"dominating_set": [1, 5, 6, 7, 8, 9, 11, 13, 20, 22, 23, 24, 27, 28, 29]} | 1 |
construct-nppc-dominating-set-l2-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 138 edges:
[[0, 1], [0, 5], [0, 9], [0, 12], [0, 14], [0, 16], [0, 18], [0, 20], [1, 6], [1, 9], [1, 10], [1, 14], [1, 15], [1, 17], [1, 20], [1, 25], [1, 26], [1, 28], [1, 29], [2, 3], [2, 5], [2, 7], [2, 9], [2, 12], [2, 23], [2, 26], [2, 27], [3, 6], [3, 11], [3, ... | {"num_nodes": 30, "k": 15, "edges": [[0, 1], [0, 5], [0, 9], [0, 12], [0, 14], [0, 16], [0, 18], [0, 20], [1, 6], [1, 9], [1, 10], [1, 14], [1, 15], [1, 17], [1, 20], [1, 25], [1, 26], [1, 28], [1, 29], [2, 3], [2, 5], [2, 7], [2, 9], [2, 12], [2, 23], [2, 26], [2, 27], [3, 6], [3, 11], [3, 15], [3, 18], [3, 21], [3, 2... | null | null | null | {"dominating_set": [1, 2, 4, 5, 6, 7, 8, 9, 11, 14, 21, 22, 25, 26, 28]} | 1 |
construct-nppc-dominating-set-l2-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 159 edges:
[[0, 1], [0, 4], [0, 5], [0, 10], [0, 11], [0, 22], [1, 2], [1, 4], [1, 6], [1, 10], [1, 13], [1, 14], [1, 16], [1, 18], [1, 20], [1, 26], [2, 8], [2, 10], [2, 13], [2, 25], [2, 27], [2, 28], [2, 29], [3, 4], [3, 5], [3, 13], [3, 14], [3, 15], [3, 16], [3,... | {"num_nodes": 30, "k": 15, "edges": [[0, 1], [0, 4], [0, 5], [0, 10], [0, 11], [0, 22], [1, 2], [1, 4], [1, 6], [1, 10], [1, 13], [1, 14], [1, 16], [1, 18], [1, 20], [1, 26], [2, 8], [2, 10], [2, 13], [2, 25], [2, 27], [2, 28], [2, 29], [3, 4], [3, 5], [3, 13], [3, 14], [3, 15], [3, 16], [3, 18], [3, 21], [3, 22], [3, ... | null | null | null | {"dominating_set": [1, 4, 5, 11, 13, 14, 15, 16, 19, 20, 23, 24, 26, 28, 29]} | 1 |
construct-nppc-dominating-set-l2-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 142 edges:
[[0, 4], [0, 11], [0, 16], [0, 20], [0, 28], [1, 2], [1, 3], [1, 8], [1, 9], [1, 10], [1, 16], [1, 21], [1, 22], [2, 7], [2, 12], [2, 15], [2, 27], [3, 4], [3, 6], [3, 10], [3, 15], [3, 17], [3, 19], [3, 22], [4, 6], [4, 10], [4, 19], [4, 20], [4, 23], [4,... | {"num_nodes": 30, "k": 15, "edges": [[0, 4], [0, 11], [0, 16], [0, 20], [0, 28], [1, 2], [1, 3], [1, 8], [1, 9], [1, 10], [1, 16], [1, 21], [1, 22], [2, 7], [2, 12], [2, 15], [2, 27], [3, 4], [3, 6], [3, 10], [3, 15], [3, 17], [3, 19], [3, 22], [4, 6], [4, 10], [4, 19], [4, 20], [4, 23], [4, 25], [4, 27], [4, 28], [4, ... | null | null | null | {"dominating_set": [1, 4, 6, 8, 9, 11, 12, 14, 15, 17, 18, 23, 24, 26, 29]} | 1 |
construct-nppc-dominating-set-l2-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 130 edges:
[[0, 4], [0, 5], [0, 10], [0, 13], [0, 17], [0, 18], [0, 19], [0, 26], [1, 2], [1, 3], [1, 4], [1, 6], [1, 15], [1, 18], [1, 26], [1, 29], [2, 4], [2, 5], [2, 6], [2, 7], [2, 13], [2, 16], [2, 19], [2, 23], [2, 24], [2, 28], [2, 29], [3, 9], [3, 10], [3, 1... | {"num_nodes": 30, "k": 15, "edges": [[0, 4], [0, 5], [0, 10], [0, 13], [0, 17], [0, 18], [0, 19], [0, 26], [1, 2], [1, 3], [1, 4], [1, 6], [1, 15], [1, 18], [1, 26], [1, 29], [2, 4], [2, 5], [2, 6], [2, 7], [2, 13], [2, 16], [2, 19], [2, 23], [2, 24], [2, 28], [2, 29], [3, 9], [3, 10], [3, 14], [3, 15], [3, 16], [3, 17... | null | null | null | {"dominating_set": [1, 2, 4, 6, 7, 8, 10, 15, 18, 19, 20, 22, 23, 24, 27]} | 1 |
construct-nppc-dominating-set-l2-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 2 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 30 vertices labelled 0..29 and 133 edges:
[[0, 2], [0, 10], [0, 16], [0, 21], [0, 22], [0, 23], [0, 28], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 10], [1, 11], [1, 12], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 26], [1, 27], [2, 4], [2, 7], [2, 10], [2, 11], [2, 17], [2, 18], [2, 24], [2... | {"num_nodes": 30, "k": 15, "edges": [[0, 2], [0, 10], [0, 16], [0, 21], [0, 22], [0, 23], [0, 28], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 10], [1, 11], [1, 12], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 26], [1, 27], [2, 4], [2, 7], [2, 10], [2, 11], [2, 17], [2, 18], [2, 24], [2, 25], [2, 29], [3, 5], [3, ... | null | null | null | {"dominating_set": [0, 1, 5, 7, 8, 10, 11, 15, 19, 20, 21, 22, 23, 24, 25]} | 1 |
construct-nppc-dominating-set-l3-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 389 edges:
[[0, 8], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 23], [0, 26], [0, 28], [0, 29], [0, 33], [0, 35], [0, 36], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [1, 4], [1, 5], [1, 8], [1, 13], [1, 20], [1, 21], [1, 23], [1, 24], [1, 25], [1, 27]... | {"num_nodes": 50, "k": 20, "edges": [[0, 8], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 23], [0, 26], [0, 28], [0, 29], [0, 33], [0, 35], [0, 36], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [1, 4], [1, 5], [1, 8], [1, 13], [1, 20], [1, 21], [1, 23], [1, 24], [1, 25], [1, 27], [1, 28], [1, 36], [1, 39],... | null | null | null | {"dominating_set": [0, 3, 5, 6, 7, 10, 14, 19, 20, 21, 23, 24, 26, 29, 34, 35, 38, 40, 44, 48]} | 1 |
construct-nppc-dominating-set-l3-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 388 edges:
[[0, 5], [0, 6], [0, 7], [0, 8], [0, 11], [0, 12], [0, 16], [0, 17], [0, 22], [0, 23], [0, 28], [0, 33], [0, 35], [0, 38], [0, 41], [0, 43], [0, 47], [1, 3], [1, 6], [1, 9], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 21], [1, 22], [1, 28], [1, 30], [... | {"num_nodes": 50, "k": 20, "edges": [[0, 5], [0, 6], [0, 7], [0, 8], [0, 11], [0, 12], [0, 16], [0, 17], [0, 22], [0, 23], [0, 28], [0, 33], [0, 35], [0, 38], [0, 41], [0, 43], [0, 47], [1, 3], [1, 6], [1, 9], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 21], [1, 22], [1, 28], [1, 30], [1, 33], [1, 35], [1, 42], [1... | null | null | null | {"dominating_set": [2, 6, 9, 11, 12, 13, 14, 15, 18, 21, 24, 26, 30, 41, 43, 44, 45, 46, 47, 49]} | 1 |
construct-nppc-dominating-set-l3-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 399 edges:
[[0, 2], [0, 6], [0, 9], [0, 10], [0, 11], [0, 14], [0, 22], [0, 26], [0, 30], [0, 36], [0, 39], [0, 43], [0, 47], [1, 2], [1, 5], [1, 6], [1, 11], [1, 12], [1, 13], [1, 14], [1, 18], [1, 21], [1, 23], [1, 25], [1, 30], [1, 33], [1, 34], [1, 35], [1, 37], ... | {"num_nodes": 50, "k": 20, "edges": [[0, 2], [0, 6], [0, 9], [0, 10], [0, 11], [0, 14], [0, 22], [0, 26], [0, 30], [0, 36], [0, 39], [0, 43], [0, 47], [1, 2], [1, 5], [1, 6], [1, 11], [1, 12], [1, 13], [1, 14], [1, 18], [1, 21], [1, 23], [1, 25], [1, 30], [1, 33], [1, 34], [1, 35], [1, 37], [1, 38], [1, 42], [2, 3], [2... | null | null | null | {"dominating_set": [0, 1, 5, 6, 8, 12, 13, 19, 23, 28, 30, 32, 36, 37, 39, 40, 41, 43, 44, 46]} | 1 |
construct-nppc-dominating-set-l3-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 375 edges:
[[0, 2], [0, 3], [0, 5], [0, 9], [0, 12], [0, 21], [0, 24], [0, 30], [0, 32], [0, 34], [0, 38], [0, 39], [0, 42], [0, 44], [0, 45], [0, 48], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 14], [1, 15], [1, 16], [1, 17], [1, 24], [1, 25], [1, 29], [1, 30], [1,... | {"num_nodes": 50, "k": 20, "edges": [[0, 2], [0, 3], [0, 5], [0, 9], [0, 12], [0, 21], [0, 24], [0, 30], [0, 32], [0, 34], [0, 38], [0, 39], [0, 42], [0, 44], [0, 45], [0, 48], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 14], [1, 15], [1, 16], [1, 17], [1, 24], [1, 25], [1, 29], [1, 30], [1, 31], [1, 33], [1, 38], [1, ... | null | null | null | {"dominating_set": [1, 9, 10, 13, 16, 21, 23, 24, 26, 30, 31, 33, 35, 36, 37, 38, 42, 45, 46, 49]} | 1 |
construct-nppc-dominating-set-l3-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 372 edges:
[[0, 2], [0, 3], [0, 8], [0, 13], [0, 14], [0, 18], [0, 19], [0, 29], [0, 30], [0, 31], [0, 36], [0, 38], [0, 40], [0, 41], [1, 11], [1, 16], [1, 18], [1, 19], [1, 22], [1, 27], [1, 34], [1, 36], [1, 42], [1, 47], [2, 4], [2, 6], [2, 7], [2, 9], [2, 11], [... | {"num_nodes": 50, "k": 20, "edges": [[0, 2], [0, 3], [0, 8], [0, 13], [0, 14], [0, 18], [0, 19], [0, 29], [0, 30], [0, 31], [0, 36], [0, 38], [0, 40], [0, 41], [1, 11], [1, 16], [1, 18], [1, 19], [1, 22], [1, 27], [1, 34], [1, 36], [1, 42], [1, 47], [2, 4], [2, 6], [2, 7], [2, 9], [2, 11], [2, 15], [2, 20], [2, 21], [2... | null | null | null | {"dominating_set": [0, 1, 4, 7, 8, 9, 12, 14, 19, 21, 23, 26, 27, 28, 30, 31, 32, 41, 42, 49]} | 1 |
construct-nppc-dominating-set-l3-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 382 edges:
[[0, 2], [0, 4], [0, 5], [0, 8], [0, 10], [0, 19], [0, 20], [0, 22], [0, 23], [0, 25], [0, 27], [0, 28], [0, 31], [0, 35], [0, 36], [0, 38], [0, 39], [0, 40], [0, 42], [0, 49], [1, 6], [1, 9], [1, 10], [1, 13], [1, 17], [1, 19], [1, 23], [1, 27], [1, 36], ... | {"num_nodes": 50, "k": 20, "edges": [[0, 2], [0, 4], [0, 5], [0, 8], [0, 10], [0, 19], [0, 20], [0, 22], [0, 23], [0, 25], [0, 27], [0, 28], [0, 31], [0, 35], [0, 36], [0, 38], [0, 39], [0, 40], [0, 42], [0, 49], [1, 6], [1, 9], [1, 10], [1, 13], [1, 17], [1, 19], [1, 23], [1, 27], [1, 36], [1, 37], [1, 39], [1, 41], [... | null | null | null | {"dominating_set": [1, 2, 4, 5, 9, 10, 11, 12, 13, 16, 17, 19, 20, 23, 26, 28, 33, 34, 42, 48]} | 1 |
construct-nppc-dominating-set-l3-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 389 edges:
[[0, 1], [0, 2], [0, 7], [0, 8], [0, 10], [0, 27], [0, 28], [0, 30], [0, 31], [0, 35], [0, 43], [0, 44], [0, 48], [1, 4], [1, 10], [1, 11], [1, 17], [1, 18], [1, 21], [1, 29], [1, 32], [1, 35], [1, 37], [1, 41], [1, 42], [1, 43], [1, 44], [2, 3], [2, 5], [... | {"num_nodes": 50, "k": 20, "edges": [[0, 1], [0, 2], [0, 7], [0, 8], [0, 10], [0, 27], [0, 28], [0, 30], [0, 31], [0, 35], [0, 43], [0, 44], [0, 48], [1, 4], [1, 10], [1, 11], [1, 17], [1, 18], [1, 21], [1, 29], [1, 32], [1, 35], [1, 37], [1, 41], [1, 42], [1, 43], [1, 44], [2, 3], [2, 5], [2, 9], [2, 23], [2, 26], [2,... | null | null | null | {"dominating_set": [0, 2, 6, 8, 9, 11, 17, 19, 20, 22, 25, 28, 31, 35, 37, 39, 44, 45, 46, 49]} | 1 |
construct-nppc-dominating-set-l3-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 384 edges:
[[0, 1], [0, 6], [0, 9], [0, 13], [0, 19], [0, 20], [0, 22], [0, 26], [0, 27], [0, 34], [0, 35], [0, 37], [0, 39], [0, 42], [1, 6], [1, 11], [1, 13], [1, 15], [1, 19], [1, 22], [1, 24], [1, 26], [1, 28], [1, 34], [1, 36], [1, 38], [1, 40], [1, 48], [2, 3],... | {"num_nodes": 50, "k": 20, "edges": [[0, 1], [0, 6], [0, 9], [0, 13], [0, 19], [0, 20], [0, 22], [0, 26], [0, 27], [0, 34], [0, 35], [0, 37], [0, 39], [0, 42], [1, 6], [1, 11], [1, 13], [1, 15], [1, 19], [1, 22], [1, 24], [1, 26], [1, 28], [1, 34], [1, 36], [1, 38], [1, 40], [1, 48], [2, 3], [2, 6], [2, 11], [2, 14], [... | null | null | null | {"dominating_set": [1, 4, 6, 9, 16, 18, 21, 22, 31, 32, 34, 35, 36, 37, 39, 41, 43, 44, 45, 47]} | 1 |
construct-nppc-dominating-set-l3-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 371 edges:
[[0, 2], [0, 5], [0, 6], [0, 13], [0, 15], [0, 18], [0, 19], [0, 27], [0, 28], [0, 30], [0, 34], [0, 37], [0, 38], [0, 41], [0, 42], [0, 46], [0, 47], [0, 48], [0, 49], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 15], [1, 18], [1, 19], [1, 23], [1, 28], [... | {"num_nodes": 50, "k": 20, "edges": [[0, 2], [0, 5], [0, 6], [0, 13], [0, 15], [0, 18], [0, 19], [0, 27], [0, 28], [0, 30], [0, 34], [0, 37], [0, 38], [0, 41], [0, 42], [0, 46], [0, 47], [0, 48], [0, 49], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 15], [1, 18], [1, 19], [1, 23], [1, 28], [1, 29], [1, 35], [1, 40], [1... | null | null | null | {"dominating_set": [1, 3, 5, 9, 13, 16, 19, 20, 21, 22, 27, 28, 34, 35, 36, 38, 40, 43, 44, 49]} | 1 |
construct-nppc-dominating-set-l3-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 3 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 50 vertices labelled 0..49 and 379 edges:
[[0, 1], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 12], [0, 19], [0, 22], [0, 25], [0, 26], [0, 28], [0, 30], [0, 31], [0, 32], [0, 34], [0, 38], [0, 39], [0, 43], [0, 45], [0, 48], [1, 4], [1, 7], [1, 8], [1, 11], [1, 12], [1, 21], [1, 23], [1, 27], [1,... | {"num_nodes": 50, "k": 20, "edges": [[0, 1], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 12], [0, 19], [0, 22], [0, 25], [0, 26], [0, 28], [0, 30], [0, 31], [0, 32], [0, 34], [0, 38], [0, 39], [0, 43], [0, 45], [0, 48], [1, 4], [1, 7], [1, 8], [1, 11], [1, 12], [1, 21], [1, 23], [1, 27], [1, 28], [1, 35], [1, 37], [1, ... | null | null | null | {"dominating_set": [0, 1, 4, 6, 7, 9, 10, 11, 14, 15, 16, 19, 20, 21, 23, 33, 35, 36, 37, 49]} | 1 |
construct-nppc-dominating-set-l4-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1552 edges:
[[0, 6], [0, 11], [0, 13], [0, 15], [0, 21], [0, 24], [0, 29], [0, 30], [0, 32], [0, 38], [0, 42], [0, 46], [0, 48], [0, 52], [0, 53], [0, 54], [0, 56], [0, 58], [0, 59], [0, 62], [0, 63], [0, 65], [0, 66], [0, 69], [0, 73], [0, 74], [0, 77], [0, 80], [0... | {"num_nodes": 100, "k": 20, "edges": [[0, 6], [0, 11], [0, 13], [0, 15], [0, 21], [0, 24], [0, 29], [0, 30], [0, 32], [0, 38], [0, 42], [0, 46], [0, 48], [0, 52], [0, 53], [0, 54], [0, 56], [0, 58], [0, 59], [0, 62], [0, 63], [0, 65], [0, 66], [0, 69], [0, 73], [0, 74], [0, 77], [0, 80], [0, 86], [0, 87], [0, 88], [0, ... | null | null | null | {"dominating_set": [1, 4, 6, 9, 10, 28, 31, 40, 43, 56, 59, 65, 68, 76, 78, 80, 82, 90, 93, 95]} | 1 |
construct-nppc-dominating-set-l4-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1545 edges:
[[0, 4], [0, 7], [0, 9], [0, 14], [0, 15], [0, 20], [0, 22], [0, 23], [0, 25], [0, 26], [0, 35], [0, 37], [0, 38], [0, 39], [0, 40], [0, 45], [0, 47], [0, 57], [0, 63], [0, 66], [0, 68], [0, 73], [0, 74], [0, 76], [0, 77], [0, 82], [0, 83], [0, 85], [0, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 4], [0, 7], [0, 9], [0, 14], [0, 15], [0, 20], [0, 22], [0, 23], [0, 25], [0, 26], [0, 35], [0, 37], [0, 38], [0, 39], [0, 40], [0, 45], [0, 47], [0, 57], [0, 63], [0, 66], [0, 68], [0, 73], [0, 74], [0, 76], [0, 77], [0, 82], [0, 83], [0, 85], [0, 87], [0, 92], [0, 93], [0, 96... | null | null | null | {"dominating_set": [0, 2, 5, 8, 10, 14, 19, 31, 38, 41, 42, 53, 55, 56, 62, 64, 68, 71, 83, 84]} | 1 |
construct-nppc-dominating-set-l4-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1509 edges:
[[0, 2], [0, 7], [0, 9], [0, 11], [0, 12], [0, 25], [0, 28], [0, 29], [0, 30], [0, 31], [0, 35], [0, 38], [0, 40], [0, 42], [0, 47], [0, 50], [0, 52], [0, 64], [0, 67], [0, 68], [0, 76], [0, 77], [0, 81], [0, 82], [0, 83], [0, 84], [0, 89], [0, 90], [1, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 2], [0, 7], [0, 9], [0, 11], [0, 12], [0, 25], [0, 28], [0, 29], [0, 30], [0, 31], [0, 35], [0, 38], [0, 40], [0, 42], [0, 47], [0, 50], [0, 52], [0, 64], [0, 67], [0, 68], [0, 76], [0, 77], [0, 81], [0, 82], [0, 83], [0, 84], [0, 89], [0, 90], [1, 5], [1, 6], [1, 8], [1, 16], ... | null | null | null | {"dominating_set": [3, 6, 9, 21, 34, 36, 48, 55, 57, 64, 65, 66, 70, 71, 73, 74, 77, 79, 83, 89]} | 1 |
construct-nppc-dominating-set-l4-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1544 edges:
[[0, 2], [0, 3], [0, 4], [0, 16], [0, 17], [0, 18], [0, 22], [0, 25], [0, 27], [0, 28], [0, 32], [0, 34], [0, 43], [0, 44], [0, 48], [0, 50], [0, 56], [0, 57], [0, 60], [0, 61], [0, 62], [0, 65], [0, 68], [0, 69], [0, 74], [0, 76], [0, 77], [0, 78], [0, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 2], [0, 3], [0, 4], [0, 16], [0, 17], [0, 18], [0, 22], [0, 25], [0, 27], [0, 28], [0, 32], [0, 34], [0, 43], [0, 44], [0, 48], [0, 50], [0, 56], [0, 57], [0, 60], [0, 61], [0, 62], [0, 65], [0, 68], [0, 69], [0, 74], [0, 76], [0, 77], [0, 78], [0, 79], [0, 86], [0, 92], [0, 93... | null | null | null | {"dominating_set": [2, 6, 14, 22, 41, 51, 52, 54, 68, 74, 78, 80, 85, 86, 87, 89, 92, 96, 97, 98]} | 1 |
construct-nppc-dominating-set-l4-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1543 edges:
[[0, 3], [0, 7], [0, 9], [0, 13], [0, 14], [0, 19], [0, 21], [0, 25], [0, 26], [0, 39], [0, 41], [0, 48], [0, 49], [0, 50], [0, 55], [0, 60], [0, 65], [0, 66], [0, 68], [0, 69], [0, 70], [0, 72], [0, 73], [0, 74], [0, 75], [0, 76], [0, 78], [0, 81], [0, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 3], [0, 7], [0, 9], [0, 13], [0, 14], [0, 19], [0, 21], [0, 25], [0, 26], [0, 39], [0, 41], [0, 48], [0, 49], [0, 50], [0, 55], [0, 60], [0, 65], [0, 66], [0, 68], [0, 69], [0, 70], [0, 72], [0, 73], [0, 74], [0, 75], [0, 76], [0, 78], [0, 81], [0, 85], [0, 88], [0, 89], [0, 90... | null | null | null | {"dominating_set": [5, 8, 13, 15, 19, 26, 29, 33, 34, 39, 45, 46, 49, 56, 70, 82, 84, 85, 92, 98]} | 1 |
construct-nppc-dominating-set-l4-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1519 edges:
[[0, 1], [0, 2], [0, 4], [0, 8], [0, 14], [0, 16], [0, 22], [0, 25], [0, 28], [0, 30], [0, 37], [0, 45], [0, 47], [0, 49], [0, 50], [0, 51], [0, 53], [0, 54], [0, 56], [0, 59], [0, 60], [0, 63], [0, 65], [0, 68], [0, 71], [0, 79], [0, 84], [0, 85], [0, 8... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 4], [0, 8], [0, 14], [0, 16], [0, 22], [0, 25], [0, 28], [0, 30], [0, 37], [0, 45], [0, 47], [0, 49], [0, 50], [0, 51], [0, 53], [0, 54], [0, 56], [0, 59], [0, 60], [0, 63], [0, 65], [0, 68], [0, 71], [0, 79], [0, 84], [0, 85], [0, 88], [0, 92], [0, 93], [0, 95]... | null | null | null | {"dominating_set": [16, 19, 28, 32, 43, 48, 49, 50, 53, 54, 55, 56, 58, 60, 64, 65, 80, 91, 93, 95]} | 1 |
construct-nppc-dominating-set-l4-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1588 edges:
[[0, 1], [0, 2], [0, 6], [0, 8], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 18], [0, 19], [0, 22], [0, 26], [0, 27], [0, 31], [0, 39], [0, 41], [0, 43], [0, 49], [0, 51], [0, 56], [0, 63], [0, 64], [0, 67], [0, 68], [0, 70], [0, 72], [0, 78], [0, 8... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 6], [0, 8], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 18], [0, 19], [0, 22], [0, 26], [0, 27], [0, 31], [0, 39], [0, 41], [0, 43], [0, 49], [0, 51], [0, 56], [0, 63], [0, 64], [0, 67], [0, 68], [0, 70], [0, 72], [0, 78], [0, 80], [0, 87], [0, 89], [0, 94]... | null | null | null | {"dominating_set": [6, 26, 29, 31, 35, 36, 37, 40, 43, 48, 49, 51, 54, 57, 60, 77, 83, 85, 88, 90]} | 1 |
construct-nppc-dominating-set-l4-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1484 edges:
[[0, 2], [0, 6], [0, 7], [0, 8], [0, 23], [0, 29], [0, 32], [0, 34], [0, 40], [0, 46], [0, 48], [0, 54], [0, 57], [0, 62], [0, 64], [0, 65], [0, 66], [0, 69], [0, 71], [0, 73], [0, 83], [0, 91], [0, 92], [0, 95], [1, 5], [1, 13], [1, 18], [1, 19], [1, 20... | {"num_nodes": 100, "k": 20, "edges": [[0, 2], [0, 6], [0, 7], [0, 8], [0, 23], [0, 29], [0, 32], [0, 34], [0, 40], [0, 46], [0, 48], [0, 54], [0, 57], [0, 62], [0, 64], [0, 65], [0, 66], [0, 69], [0, 71], [0, 73], [0, 83], [0, 91], [0, 92], [0, 95], [1, 5], [1, 13], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24],... | null | null | null | {"dominating_set": [0, 11, 19, 21, 25, 36, 46, 47, 51, 54, 59, 65, 69, 74, 80, 84, 85, 86, 89, 98]} | 1 |
construct-nppc-dominating-set-l4-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1651 edges:
[[0, 1], [0, 2], [0, 3], [0, 7], [0, 13], [0, 16], [0, 17], [0, 18], [0, 20], [0, 26], [0, 27], [0, 34], [0, 39], [0, 43], [0, 44], [0, 47], [0, 49], [0, 51], [0, 53], [0, 54], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 72], [0, 73], [0, 75], [0, 8... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 7], [0, 13], [0, 16], [0, 17], [0, 18], [0, 20], [0, 26], [0, 27], [0, 34], [0, 39], [0, 43], [0, 44], [0, 47], [0, 49], [0, 51], [0, 53], [0, 54], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 72], [0, 73], [0, 75], [0, 80], [0, 82], [0, 84], [0, 86]... | null | null | null | {"dominating_set": [3, 25, 32, 36, 42, 46, 47, 49, 60, 68, 70, 71, 73, 75, 80, 81, 83, 88, 91, 99]} | 1 |
construct-nppc-dominating-set-l4-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 4 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 100 vertices labelled 0..99 and 1536 edges:
[[0, 1], [0, 7], [0, 9], [0, 17], [0, 18], [0, 21], [0, 22], [0, 25], [0, 35], [0, 36], [0, 39], [0, 51], [0, 52], [0, 54], [0, 58], [0, 59], [0, 63], [0, 64], [0, 66], [0, 72], [0, 73], [0, 75], [0, 76], [0, 79], [0, 86], [0, 90], [0, 92], [0, 99], [1, ... | {"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 7], [0, 9], [0, 17], [0, 18], [0, 21], [0, 22], [0, 25], [0, 35], [0, 36], [0, 39], [0, 51], [0, 52], [0, 54], [0, 58], [0, 59], [0, 63], [0, 64], [0, 66], [0, 72], [0, 73], [0, 75], [0, 76], [0, 79], [0, 86], [0, 90], [0, 92], [0, 99], [1, 7], [1, 10], [1, 11], [1, 12]... | null | null | null | {"dominating_set": [11, 20, 21, 25, 26, 29, 38, 41, 54, 57, 60, 64, 67, 75, 76, 82, 90, 94, 96, 97]} | 1 |
construct-nppc-dominating-set-l5-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3333 edges:
[[0, 5], [0, 8], [0, 16], [0, 17], [0, 33], [0, 39], [0, 43], [0, 61], [0, 66], [0, 69], [0, 74], [0, 77], [0, 79], [0, 85], [0, 89], [0, 93], [0, 94], [0, 102], [0, 112], [0, 128], [0, 129], [0, 132], [0, 137], [0, 138], [0, 143], [0, 144], [0, 147], [... | {"num_nodes": 180, "k": 15, "edges": [[0, 5], [0, 8], [0, 16], [0, 17], [0, 33], [0, 39], [0, 43], [0, 61], [0, 66], [0, 69], [0, 74], [0, 77], [0, 79], [0, 85], [0, 89], [0, 93], [0, 94], [0, 102], [0, 112], [0, 128], [0, 129], [0, 132], [0, 137], [0, 138], [0, 143], [0, 144], [0, 147], [0, 156], [0, 157], [0, 158], [... | null | null | null | {"dominating_set": [3, 36, 62, 66, 67, 68, 72, 93, 100, 118, 124, 140, 145, 169, 178]} | 1 |
construct-nppc-dominating-set-l5-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3379 edges:
[[0, 16], [0, 20], [0, 25], [0, 26], [0, 35], [0, 38], [0, 41], [0, 42], [0, 60], [0, 65], [0, 69], [0, 71], [0, 80], [0, 87], [0, 92], [0, 97], [0, 102], [0, 105], [0, 106], [0, 110], [0, 111], [0, 116], [0, 118], [0, 126], [0, 128], [0, 134], [0, 139]... | {"num_nodes": 180, "k": 15, "edges": [[0, 16], [0, 20], [0, 25], [0, 26], [0, 35], [0, 38], [0, 41], [0, 42], [0, 60], [0, 65], [0, 69], [0, 71], [0, 80], [0, 87], [0, 92], [0, 97], [0, 102], [0, 105], [0, 106], [0, 110], [0, 111], [0, 116], [0, 118], [0, 126], [0, 128], [0, 134], [0, 139], [0, 143], [0, 150], [0, 158]... | null | null | null | {"dominating_set": [13, 58, 65, 67, 68, 86, 96, 119, 122, 125, 146, 148, 153, 156, 168]} | 1 |
construct-nppc-dominating-set-l5-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3391 edges:
[[0, 1], [0, 5], [0, 11], [0, 13], [0, 18], [0, 21], [0, 29], [0, 30], [0, 35], [0, 37], [0, 49], [0, 60], [0, 62], [0, 66], [0, 69], [0, 70], [0, 71], [0, 73], [0, 76], [0, 84], [0, 89], [0, 100], [0, 103], [0, 126], [0, 133], [0, 134], [0, 143], [0, 1... | {"num_nodes": 180, "k": 15, "edges": [[0, 1], [0, 5], [0, 11], [0, 13], [0, 18], [0, 21], [0, 29], [0, 30], [0, 35], [0, 37], [0, 49], [0, 60], [0, 62], [0, 66], [0, 69], [0, 70], [0, 71], [0, 73], [0, 76], [0, 84], [0, 89], [0, 100], [0, 103], [0, 126], [0, 133], [0, 134], [0, 143], [0, 147], [0, 155], [0, 168], [0, 1... | null | null | null | {"dominating_set": [20, 39, 50, 58, 61, 62, 63, 85, 104, 123, 133, 141, 146, 167, 168]} | 1 |
construct-nppc-dominating-set-l5-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3291 edges:
[[0, 4], [0, 13], [0, 21], [0, 22], [0, 23], [0, 28], [0, 32], [0, 37], [0, 38], [0, 48], [0, 49], [0, 55], [0, 68], [0, 78], [0, 82], [0, 84], [0, 86], [0, 87], [0, 88], [0, 99], [0, 102], [0, 103], [0, 107], [0, 110], [0, 122], [0, 123], [0, 127], [0,... | {"num_nodes": 180, "k": 15, "edges": [[0, 4], [0, 13], [0, 21], [0, 22], [0, 23], [0, 28], [0, 32], [0, 37], [0, 38], [0, 48], [0, 49], [0, 55], [0, 68], [0, 78], [0, 82], [0, 84], [0, 86], [0, 87], [0, 88], [0, 99], [0, 102], [0, 103], [0, 107], [0, 110], [0, 122], [0, 123], [0, 127], [0, 130], [0, 132], [0, 134], [0,... | null | null | null | {"dominating_set": [9, 13, 25, 27, 30, 48, 49, 56, 107, 127, 129, 130, 139, 151, 153]} | 1 |
construct-nppc-dominating-set-l5-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3386 edges:
[[0, 8], [0, 14], [0, 16], [0, 30], [0, 31], [0, 32], [0, 34], [0, 43], [0, 47], [0, 48], [0, 55], [0, 65], [0, 75], [0, 80], [0, 84], [0, 91], [0, 93], [0, 96], [0, 98], [0, 105], [0, 108], [0, 111], [0, 118], [0, 127], [0, 137], [0, 142], [0, 143], [0... | {"num_nodes": 180, "k": 15, "edges": [[0, 8], [0, 14], [0, 16], [0, 30], [0, 31], [0, 32], [0, 34], [0, 43], [0, 47], [0, 48], [0, 55], [0, 65], [0, 75], [0, 80], [0, 84], [0, 91], [0, 93], [0, 96], [0, 98], [0, 105], [0, 108], [0, 111], [0, 118], [0, 127], [0, 137], [0, 142], [0, 143], [0, 146], [0, 150], [0, 158], [0... | null | null | null | {"dominating_set": [3, 5, 11, 20, 55, 58, 78, 79, 101, 109, 113, 125, 140, 149, 169]} | 1 |
construct-nppc-dominating-set-l5-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3266 edges:
[[0, 1], [0, 9], [0, 16], [0, 18], [0, 21], [0, 32], [0, 33], [0, 36], [0, 39], [0, 40], [0, 44], [0, 47], [0, 52], [0, 58], [0, 63], [0, 72], [0, 73], [0, 75], [0, 76], [0, 77], [0, 80], [0, 86], [0, 93], [0, 97], [0, 103], [0, 105], [0, 108], [0, 111]... | {"num_nodes": 180, "k": 15, "edges": [[0, 1], [0, 9], [0, 16], [0, 18], [0, 21], [0, 32], [0, 33], [0, 36], [0, 39], [0, 40], [0, 44], [0, 47], [0, 52], [0, 58], [0, 63], [0, 72], [0, 73], [0, 75], [0, 76], [0, 77], [0, 80], [0, 86], [0, 93], [0, 97], [0, 103], [0, 105], [0, 108], [0, 111], [0, 112], [0, 113], [0, 119]... | null | null | null | {"dominating_set": [12, 23, 37, 39, 68, 69, 74, 83, 92, 96, 97, 111, 116, 151, 170]} | 1 |
construct-nppc-dominating-set-l5-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3266 edges:
[[0, 4], [0, 6], [0, 8], [0, 9], [0, 13], [0, 19], [0, 45], [0, 47], [0, 52], [0, 63], [0, 64], [0, 73], [0, 95], [0, 96], [0, 99], [0, 101], [0, 103], [0, 121], [0, 132], [0, 143], [0, 153], [0, 160], [0, 168], [0, 175], [0, 176], [1, 5], [1, 7], [1, 9... | {"num_nodes": 180, "k": 15, "edges": [[0, 4], [0, 6], [0, 8], [0, 9], [0, 13], [0, 19], [0, 45], [0, 47], [0, 52], [0, 63], [0, 64], [0, 73], [0, 95], [0, 96], [0, 99], [0, 101], [0, 103], [0, 121], [0, 132], [0, 143], [0, 153], [0, 160], [0, 168], [0, 175], [0, 176], [1, 5], [1, 7], [1, 9], [1, 10], [1, 17], [1, 22], ... | null | null | null | {"dominating_set": [1, 8, 10, 26, 36, 58, 70, 71, 99, 101, 108, 115, 135, 159, 165]} | 1 |
construct-nppc-dominating-set-l5-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3310 edges:
[[0, 8], [0, 20], [0, 27], [0, 31], [0, 35], [0, 42], [0, 43], [0, 55], [0, 56], [0, 57], [0, 58], [0, 66], [0, 71], [0, 73], [0, 76], [0, 99], [0, 100], [0, 108], [0, 118], [0, 121], [0, 124], [0, 126], [0, 136], [0, 137], [0, 140], [0, 146], [0, 147],... | {"num_nodes": 180, "k": 15, "edges": [[0, 8], [0, 20], [0, 27], [0, 31], [0, 35], [0, 42], [0, 43], [0, 55], [0, 56], [0, 57], [0, 58], [0, 66], [0, 71], [0, 73], [0, 76], [0, 99], [0, 100], [0, 108], [0, 118], [0, 121], [0, 124], [0, 126], [0, 136], [0, 137], [0, 140], [0, 146], [0, 147], [0, 148], [0, 155], [0, 156],... | null | null | null | {"dominating_set": [1, 29, 34, 37, 45, 84, 89, 134, 136, 138, 139, 146, 148, 165, 177]} | 1 |
construct-nppc-dominating-set-l5-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3296 edges:
[[0, 2], [0, 8], [0, 14], [0, 15], [0, 20], [0, 21], [0, 22], [0, 28], [0, 29], [0, 31], [0, 34], [0, 37], [0, 39], [0, 46], [0, 49], [0, 52], [0, 57], [0, 58], [0, 67], [0, 76], [0, 80], [0, 91], [0, 93], [0, 99], [0, 113], [0, 117], [0, 118], [0, 122]... | {"num_nodes": 180, "k": 15, "edges": [[0, 2], [0, 8], [0, 14], [0, 15], [0, 20], [0, 21], [0, 22], [0, 28], [0, 29], [0, 31], [0, 34], [0, 37], [0, 39], [0, 46], [0, 49], [0, 52], [0, 57], [0, 58], [0, 67], [0, 76], [0, 80], [0, 91], [0, 93], [0, 99], [0, 113], [0, 117], [0, 118], [0, 122], [0, 128], [0, 140], [0, 146]... | null | null | null | {"dominating_set": [3, 6, 27, 50, 65, 67, 68, 76, 96, 103, 126, 134, 136, 146, 150]} | 1 |
construct-nppc-dominating-set-l5-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 5 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 180 vertices labelled 0..179 and 3330 edges:
[[0, 3], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 26], [0, 38], [0, 39], [0, 53], [0, 65], [0, 68], [0, 71], [0, 78], [0, 95], [0, 97], [0, 100], [0, 101], [0, 106], [0, 116], [0, 123], [0, 127], [0, 128], [0, 131], [0, 133], [0, 135], [0, 143],... | {"num_nodes": 180, "k": 15, "edges": [[0, 3], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 26], [0, 38], [0, 39], [0, 53], [0, 65], [0, 68], [0, 71], [0, 78], [0, 95], [0, 97], [0, 100], [0, 101], [0, 106], [0, 116], [0, 123], [0, 127], [0, 128], [0, 131], [0, 133], [0, 135], [0, 143], [0, 147], [0, 148], [0, 153],... | null | null | null | {"dominating_set": [4, 26, 42, 43, 45, 84, 92, 106, 122, 128, 131, 141, 154, 167, 170]} | 1 |
construct-nppc-dominating-set-l6-s0 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2982 edges:
[[0, 6], [0, 12], [0, 19], [0, 21], [0, 61], [0, 68], [0, 99], [0, 112], [0, 131], [0, 137], [0, 143], [0, 159], [0, 163], [0, 195], [0, 196], [0, 214], [0, 217], [0, 225], [0, 241], [0, 253], [0, 264], [1, 11], [1, 41], [1, 52], [1, 62], [1, 94], [1, 1... | {"num_nodes": 300, "k": 20, "edges": [[0, 6], [0, 12], [0, 19], [0, 21], [0, 61], [0, 68], [0, 99], [0, 112], [0, 131], [0, 137], [0, 143], [0, 159], [0, 163], [0, 195], [0, 196], [0, 214], [0, 217], [0, 225], [0, 241], [0, 253], [0, 264], [1, 11], [1, 41], [1, 52], [1, 62], [1, 94], [1, 107], [1, 145], [1, 158], [1, 1... | null | null | null | {"dominating_set": [31, 40, 62, 64, 75, 85, 90, 118, 131, 151, 179, 200, 208, 210, 212, 214, 218, 221, 260, 277]} | 1 |
construct-nppc-dominating-set-l6-s1 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2930 edges:
[[0, 12], [0, 29], [0, 36], [0, 41], [0, 52], [0, 93], [0, 111], [0, 149], [0, 153], [0, 158], [0, 195], [0, 266], [0, 277], [0, 281], [1, 7], [1, 19], [1, 30], [1, 56], [1, 60], [1, 69], [1, 97], [1, 148], [1, 153], [1, 172], [1, 181], [1, 231], [1, 24... | {"num_nodes": 300, "k": 20, "edges": [[0, 12], [0, 29], [0, 36], [0, 41], [0, 52], [0, 93], [0, 111], [0, 149], [0, 153], [0, 158], [0, 195], [0, 266], [0, 277], [0, 281], [1, 7], [1, 19], [1, 30], [1, 56], [1, 60], [1, 69], [1, 97], [1, 148], [1, 153], [1, 172], [1, 181], [1, 231], [1, 240], [1, 259], [1, 269], [1, 27... | null | null | null | {"dominating_set": [10, 16, 25, 30, 36, 56, 68, 81, 98, 102, 121, 132, 141, 156, 175, 193, 199, 220, 228, 269]} | 1 |
construct-nppc-dominating-set-l6-s2 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2957 edges:
[[0, 8], [0, 12], [0, 40], [0, 44], [0, 79], [0, 80], [0, 86], [0, 141], [0, 145], [0, 148], [0, 176], [0, 205], [0, 212], [0, 244], [0, 282], [0, 287], [1, 12], [1, 17], [1, 21], [1, 25], [1, 34], [1, 91], [1, 98], [1, 104], [1, 108], [1, 137], [1, 159... | {"num_nodes": 300, "k": 20, "edges": [[0, 8], [0, 12], [0, 40], [0, 44], [0, 79], [0, 80], [0, 86], [0, 141], [0, 145], [0, 148], [0, 176], [0, 205], [0, 212], [0, 244], [0, 282], [0, 287], [1, 12], [1, 17], [1, 21], [1, 25], [1, 34], [1, 91], [1, 98], [1, 104], [1, 108], [1, 137], [1, 159], [1, 168], [1, 179], [1, 183... | null | null | null | {"dominating_set": [21, 38, 52, 60, 67, 70, 95, 111, 124, 133, 137, 148, 149, 152, 164, 168, 195, 208, 255, 277]} | 1 |
construct-nppc-dominating-set-l6-s3 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2894 edges:
[[0, 20], [0, 43], [0, 51], [0, 59], [0, 67], [0, 85], [0, 100], [0, 113], [0, 115], [0, 116], [0, 122], [0, 160], [0, 180], [0, 184], [0, 195], [0, 210], [0, 243], [0, 245], [0, 247], [1, 4], [1, 17], [1, 23], [1, 31], [1, 33], [1, 44], [1, 49], [1, 85... | {"num_nodes": 300, "k": 20, "edges": [[0, 20], [0, 43], [0, 51], [0, 59], [0, 67], [0, 85], [0, 100], [0, 113], [0, 115], [0, 116], [0, 122], [0, 160], [0, 180], [0, 184], [0, 195], [0, 210], [0, 243], [0, 245], [0, 247], [1, 4], [1, 17], [1, 23], [1, 31], [1, 33], [1, 44], [1, 49], [1, 85], [1, 125], [1, 127], [1, 183... | null | null | null | {"dominating_set": [9, 79, 92, 95, 106, 116, 119, 124, 130, 141, 143, 158, 169, 178, 179, 200, 208, 215, 277, 286]} | 1 |
construct-nppc-dominating-set-l6-s4 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2978 edges:
[[0, 31], [0, 47], [0, 90], [0, 96], [0, 101], [0, 107], [0, 113], [0, 114], [0, 121], [0, 158], [0, 179], [0, 185], [0, 188], [0, 194], [0, 204], [0, 207], [0, 217], [0, 219], [0, 238], [0, 274], [1, 9], [1, 20], [1, 43], [1, 72], [1, 90], [1, 91], [1,... | {"num_nodes": 300, "k": 20, "edges": [[0, 31], [0, 47], [0, 90], [0, 96], [0, 101], [0, 107], [0, 113], [0, 114], [0, 121], [0, 158], [0, 179], [0, 185], [0, 188], [0, 194], [0, 204], [0, 207], [0, 217], [0, 219], [0, 238], [0, 274], [1, 9], [1, 20], [1, 43], [1, 72], [1, 90], [1, 91], [1, 153], [1, 178], [1, 197], [1,... | null | null | null | {"dominating_set": [8, 18, 54, 69, 76, 77, 83, 91, 101, 107, 137, 156, 161, 164, 181, 243, 245, 257, 274, 282]} | 1 |
construct-nppc-dominating-set-l6-s5 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2971 edges:
[[0, 12], [0, 25], [0, 26], [0, 37], [0, 78], [0, 102], [0, 117], [0, 185], [0, 212], [0, 242], [0, 265], [0, 282], [1, 2], [1, 23], [1, 50], [1, 130], [1, 134], [1, 139], [1, 143], [1, 146], [1, 147], [1, 188], [1, 205], [1, 207], [1, 234], [1, 297], [... | {"num_nodes": 300, "k": 20, "edges": [[0, 12], [0, 25], [0, 26], [0, 37], [0, 78], [0, 102], [0, 117], [0, 185], [0, 212], [0, 242], [0, 265], [0, 282], [1, 2], [1, 23], [1, 50], [1, 130], [1, 134], [1, 139], [1, 143], [1, 146], [1, 147], [1, 188], [1, 205], [1, 207], [1, 234], [1, 297], [2, 16], [2, 115], [2, 140], [2... | null | null | null | {"dominating_set": [15, 41, 44, 56, 61, 71, 84, 98, 100, 102, 139, 145, 185, 241, 246, 254, 264, 270, 276, 292]} | 1 |
construct-nppc-dominating-set-l6-s6 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2928 edges:
[[0, 10], [0, 33], [0, 56], [0, 78], [0, 79], [0, 86], [0, 92], [0, 94], [0, 96], [0, 109], [0, 132], [0, 168], [0, 169], [0, 175], [0, 189], [0, 218], [0, 231], [0, 240], [0, 286], [0, 292], [1, 46], [1, 70], [1, 77], [1, 95], [1, 113], [1, 133], [1, 1... | {"num_nodes": 300, "k": 20, "edges": [[0, 10], [0, 33], [0, 56], [0, 78], [0, 79], [0, 86], [0, 92], [0, 94], [0, 96], [0, 109], [0, 132], [0, 168], [0, 169], [0, 175], [0, 189], [0, 218], [0, 231], [0, 240], [0, 286], [0, 292], [1, 46], [1, 70], [1, 77], [1, 95], [1, 113], [1, 133], [1, 156], [1, 162], [1, 230], [1, 2... | null | null | null | {"dominating_set": [34, 76, 82, 85, 86, 103, 114, 116, 125, 129, 202, 216, 220, 230, 249, 255, 260, 281, 288, 289]} | 1 |
construct-nppc-dominating-set-l6-s7 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2900 edges:
[[0, 11], [0, 26], [0, 37], [0, 42], [0, 45], [0, 58], [0, 77], [0, 118], [0, 126], [0, 133], [0, 134], [0, 158], [0, 163], [0, 173], [0, 175], [0, 182], [0, 222], [0, 223], [0, 224], [0, 234], [0, 236], [0, 239], [0, 244], [0, 245], [0, 272], [0, 279],... | {"num_nodes": 300, "k": 20, "edges": [[0, 11], [0, 26], [0, 37], [0, 42], [0, 45], [0, 58], [0, 77], [0, 118], [0, 126], [0, 133], [0, 134], [0, 158], [0, 163], [0, 173], [0, 175], [0, 182], [0, 222], [0, 223], [0, 224], [0, 234], [0, 236], [0, 239], [0, 244], [0, 245], [0, 272], [0, 279], [1, 30], [1, 35], [1, 51], [1... | null | null | null | {"dominating_set": [2, 11, 14, 41, 54, 60, 82, 90, 99, 132, 143, 180, 183, 208, 236, 251, 269, 276, 277, 291]} | 1 |
construct-nppc-dominating-set-l6-s8 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2957 edges:
[[0, 8], [0, 25], [0, 32], [0, 35], [0, 40], [0, 72], [0, 93], [0, 103], [0, 107], [0, 119], [0, 123], [0, 152], [0, 163], [0, 214], [0, 217], [0, 251], [0, 284], [0, 295], [1, 6], [1, 19], [1, 30], [1, 42], [1, 52], [1, 54], [1, 64], [1, 68], [1, 74], ... | {"num_nodes": 300, "k": 20, "edges": [[0, 8], [0, 25], [0, 32], [0, 35], [0, 40], [0, 72], [0, 93], [0, 103], [0, 107], [0, 119], [0, 123], [0, 152], [0, 163], [0, 214], [0, 217], [0, 251], [0, 284], [0, 295], [1, 6], [1, 19], [1, 30], [1, 42], [1, 52], [1, 54], [1, 64], [1, 68], [1, 74], [1, 81], [1, 100], [1, 116], [... | null | null | null | {"dominating_set": [10, 24, 37, 46, 47, 55, 64, 97, 108, 137, 141, 163, 179, 194, 200, 222, 250, 253, 264, 287]} | 1 |
construct-nppc-dominating-set-l6-s9 | construct | nppc_dominating_set | graph_dominating_set | graph_theory | competition | 6 | NPPC/dominating_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 300 vertices labelled 0..299 and 2987 edges:
[[0, 1], [0, 9], [0, 44], [0, 71], [0, 75], [0, 79], [0, 92], [0, 93], [0, 100], [0, 114], [0, 124], [0, 136], [0, 157], [0, 159], [0, 175], [0, 191], [0, 193], [0, 206], [0, 212], [0, 216], [0, 250], [0, 267], [0, 270], [0, 276], [1, 32], [1, 67], [1, ... | {"num_nodes": 300, "k": 20, "edges": [[0, 1], [0, 9], [0, 44], [0, 71], [0, 75], [0, 79], [0, 92], [0, 93], [0, 100], [0, 114], [0, 124], [0, 136], [0, 157], [0, 159], [0, 175], [0, 191], [0, 193], [0, 206], [0, 212], [0, 216], [0, 250], [0, 267], [0, 270], [0, 276], [1, 32], [1, 67], [1, 68], [1, 75], [1, 78], [1, 82]... | null | null | null | {"dominating_set": [9, 35, 45, 71, 82, 97, 103, 112, 113, 127, 133, 135, 171, 197, 200, 203, 204, 237, 253, 266]} | 1 |
construct-nppc-independent-set-l1-s0 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 13 edges:
[[0, 1], [0, 6], [0, 7], [1, 2], [1, 5], [1, 7], [2, 3], [2, 4], [2, 5], [3, 7], [4, 5], [4, 7], [6, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v... | {"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 6], [0, 7], [1, 2], [1, 5], [1, 7], [2, 3], [2, 4], [2, 5], [3, 7], [4, 5], [4, 7], [6, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [1, 3, 4, 6]} | 1 |
construct-nppc-independent-set-l1-s1 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 13 edges:
[[0, 4], [0, 7], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [3, 7], [4, 7], [5, 6], [5, 7], [6, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v... | {"num_nodes": 8, "k": 4, "edges": [[0, 4], [0, 7], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [3, 7], [4, 7], [5, 6], [5, 7], [6, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 1, 3, 5]} | 1 |
construct-nppc-independent-set-l1-s2 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 9 edges:
[[0, 1], [0, 2], [0, 6], [1, 3], [2, 5], [3, 4], [3, 6], [4, 7], [6, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v_2, ...]} (at least 4 distinct in... | {"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 2], [0, 6], [1, 3], [2, 5], [3, 4], [3, 6], [4, 7], [6, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 3, 5, 7]} | 1 |
construct-nppc-independent-set-l1-s3 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 7 edges:
[[0, 1], [0, 4], [1, 4], [1, 7], [3, 4], [3, 7], [5, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v_2, ...]} (at least 4 distinct integers in 0..7).... | {"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 4], [1, 4], [1, 7], [3, 4], [3, 7], [5, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 2, 3, 5]} | 1 |
construct-nppc-independent-set-l1-s4 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 14 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [1, 2], [1, 3], [1, 7], [2, 3], [2, 4], [2, 7], [3, 5], [5, 6], [5, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set":... | {"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [1, 2], [1, 3], [1, 7], [2, 3], [2, 4], [2, 7], [3, 5], [5, 6], [5, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [3, 4, 6, 7]} | 1 |
construct-nppc-independent-set-l1-s5 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 13 edges:
[[0, 1], [0, 4], [0, 5], [0, 7], [1, 3], [1, 6], [3, 6], [3, 7], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v... | {"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 4], [0, 5], [0, 7], [1, 3], [1, 6], [3, 6], [3, 7], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [1, 2, 4, 5]} | 1 |
construct-nppc-independent-set-l1-s6 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 13 edges:
[[0, 2], [0, 3], [0, 4], [1, 2], [2, 3], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 6], [4, 7], [5, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v... | {"num_nodes": 8, "k": 4, "edges": [[0, 2], [0, 3], [0, 4], [1, 2], [2, 3], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 6], [4, 7], [5, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 1, 6, 7]} | 1 |
construct-nppc-independent-set-l1-s7 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 11 edges:
[[0, 3], [0, 4], [0, 6], [1, 3], [1, 5], [1, 6], [2, 4], [2, 6], [3, 5], [4, 7], [5, 6]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v_2, ...]} (at le... | {"num_nodes": 8, "k": 4, "edges": [[0, 3], [0, 4], [0, 6], [1, 3], [1, 5], [1, 6], [2, 4], [2, 6], [3, 5], [4, 7], [5, 6]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 1, 2, 7]} | 1 |
construct-nppc-independent-set-l1-s8 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 14 edges:
[[0, 2], [0, 3], [0, 6], [1, 2], [1, 3], [1, 6], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [4, 6], [5, 7]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set":... | {"num_nodes": 8, "k": 4, "edges": [[0, 2], [0, 3], [0, 6], [1, 2], [1, 3], [1, 6], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [4, 6], [5, 7]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 1, 4, 7]} | 1 |
construct-nppc-independent-set-l1-s9 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 1 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 9 edges:
[[0, 7], [1, 3], [1, 5], [1, 7], [2, 4], [2, 7], [4, 5], [4, 7], [5, 6]]
Find an independent set of size at least 4: a set of distinct vertices no two of which are joined by an edge.
Answer format: {"independent_set": [v_1, v_2, ...]} (at least 4 distinct in... | {"num_nodes": 8, "k": 4, "edges": [[0, 7], [1, 3], [1, 5], [1, 7], [2, 4], [2, 7], [4, 5], [4, 7], [5, 6]], "family": "nppc_independent_set", "subset": "construct"} | null | null | null | {"independent_set": [0, 1, 4, 6]} | 1 |
construct-nppc-independent-set-l2-s0 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 42 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 14], [1, 2], [1, 5], [1, 8], [1, 9], [1, 12], [1, 15], [2, 6], [3, 5], [3, 6], [3, 9], [3, 12], [3, 13], [4, 6], [4, 12], [5, 7], [5, 11], [5, 12], [5, 13], [5, 14], [6, 8], [6, 9], [6, 15], [7, 8], [7, 1... | {"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 14], [1, 2], [1, 5], [1, 8], [1, 9], [1, 12], [1, 15], [2, 6], [3, 5], [3, 6], [3, 9], [3, 12], [3, 13], [4, 6], [4, 12], [5, 7], [5, 11], [5, 12], [5, 13], [5, 14], [6, 8], [6, 9], [6, 15], [7, 8], [7, 12], [8, 9], [8, 12], [8, 14]... | null | null | null | {"independent_set": [2, 3, 4, 7, 10, 11, 14, 15]} | 1 |
construct-nppc-independent-set-l2-s1 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 47 edges:
[[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 14], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 14], [1, 15], [2, 8], [3, 5], [3, 10], [3, 11], [3, 14], [3, 15], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [4, 15], [5... | {"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 14], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 14], [1, 15], [2, 8], [3, 5], [3, 10], [3, 11], [3, 14], [3, 15], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [4, 15], [5, 14], [6, 8], [7, 12], [7, ... | null | null | null | {"independent_set": [2, 5, 6, 7, 9, 10, 11, 13]} | 1 |
construct-nppc-independent-set-l2-s2 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 44 edges:
[[0, 2], [0, 6], [0, 14], [0, 15], [1, 2], [1, 7], [1, 8], [1, 15], [2, 6], [2, 8], [2, 9], [2, 10], [2, 12], [2, 14], [2, 15], [3, 10], [3, 12], [3, 14], [4, 6], [4, 10], [4, 12], [4, 14], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 13], [5, 14], [6, 7],... | {"num_nodes": 16, "k": 8, "edges": [[0, 2], [0, 6], [0, 14], [0, 15], [1, 2], [1, 7], [1, 8], [1, 15], [2, 6], [2, 8], [2, 9], [2, 10], [2, 12], [2, 14], [2, 15], [3, 10], [3, 12], [3, 14], [4, 6], [4, 10], [4, 12], [4, 14], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 13], [5, 14], [6, 7], [6, 8], [6, 9], [6, 11], [6... | null | null | null | {"independent_set": [0, 3, 4, 7, 8, 9, 11, 13]} | 1 |
construct-nppc-independent-set-l2-s3 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 39 edges:
[[0, 1], [0, 6], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 10], [1, 13], [1, 15], [2, 3], [2, 6], [2, 12], [2, 13], [3, 9], [3, 10], [4, 5], [4, 10], [4, 12], [4, 13], [4, 14], [4, 15], [5, 6], [5, 9], [5, 10], [5, 11], [6, 9], [6, 13], [6, 14], [7, 9], [... | {"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 6], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 10], [1, 13], [1, 15], [2, 3], [2, 6], [2, 12], [2, 13], [3, 9], [3, 10], [4, 5], [4, 10], [4, 12], [4, 13], [4, 14], [4, 15], [5, 6], [5, 9], [5, 10], [5, 11], [6, 9], [6, 13], [6, 14], [7, 9], [8, 10], [8, 13], [9, 10], [9... | null | null | null | {"independent_set": [0, 3, 5, 7, 8, 12, 14, 15]} | 1 |
construct-nppc-independent-set-l2-s4 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 46 edges:
[[0, 1], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 7], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [2, 4], [2, 8], [2, 9], [2, 11], [2, 12], [2, 15], [3, 7], [3, 8], [3, 9], [3, 14], [4, 7], [4, 9], [4, 14], [5, 10], [5, 11], [5,... | {"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 7], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [2, 4], [2, 8], [2, 9], [2, 11], [2, 12], [2, 15], [3, 7], [3, 8], [3, 9], [3, 14], [4, 7], [4, 9], [4, 14], [5, 10], [5, 11], [5, 12], [5, 14], [6, 7], [6, 8... | null | null | null | {"independent_set": [3, 4, 6, 10, 11, 12, 13, 15]} | 1 |
construct-nppc-independent-set-l2-s5 | construct | nppc_independent_set | graph_independent_set | graph_theory | competition | 2 | NPPC/independent_set | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 47 edges:
[[0, 13], [0, 14], [0, 15], [1, 7], [1, 12], [2, 4], [2, 5], [2, 10], [2, 13], [2, 14], [3, 10], [3, 12], [4, 5], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [5, 7], [5, 9], [5, 11], [5, 13], [5, 14], [5, 15], [6, 10], [6, 12], [6, 13], [6, 14], [6, 15], [7,... | {"num_nodes": 16, "k": 8, "edges": [[0, 13], [0, 14], [0, 15], [1, 7], [1, 12], [2, 4], [2, 5], [2, 10], [2, 13], [2, 14], [3, 10], [3, 12], [4, 5], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [5, 7], [5, 9], [5, 11], [5, 13], [5, 14], [5, 15], [6, 10], [6, 12], [6, 13], [6, 14], [6, 15], [7, 10], [7, 12], [7, 14], [7, ... | null | null | null | {"independent_set": [0, 2, 3, 6, 7, 8, 9, 11]} | 1 |
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