{"paper":{"title":"Finding cliques using few probes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"David Gamarnik, Joe Neeman, Mikl\\'os Z. R\\'acz, Prasad Tetali, Uriel Feige","submitted_at":"2018-09-18T21:57:20Z","abstract_excerpt":"Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an $n$ vertex graph, and need to output a clique. We show that if the input graph is drawn at random from $G_{n,\\frac{1}{2}}$ (and hence is likely to have a clique of size roughly $2\\log n$), then for every $\\delta < 2$ and constant $\\ell$, there is an $\\alpha < 2$ (that may depend on $\\delta$ and $\\ell$) such that no algorithm that makes $n^{\\delta}$ probes in $\\ell$ rounds is likely (over the choice of the random graph) to output a clique of size larger than $\\alpha \\log n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06950","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}