{"paper":{"title":"Popular conjectures imply strong lower bounds for dynamic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Amir Abboud, Virginia Vassilevska Williams","submitted_at":"2014-02-01T06:20:09Z","abstract_excerpt":"We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms:\n  1. Is the 3SUM problem on $n$ numbers in $O(n^{2-\\epsilon})$ time for some $\\epsilon>0$?\n  2. Can one determine the satisfiability of a CNF formula on $n$ variables in $O((2-\\epsilon)^n poly n)$ time for some $\\epsilon>0$?\n  3. Is the All Pairs Shortest Paths problem for graphs on $n$ vertices in $O(n^{3-\\epsilon})$ time for some $\\epsilon>0$?\n  4. Is there a linear time algorithm that dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0054","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"}