{"paper":{"title":"Unifying and Strengthening Hardness for Dynamic Problems via the Online Matrix-Vector Multiplication Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danupon Nanongkai, Monika Henzinger, Sebastian Krinninger, Thatchaphol Saranurak","submitted_at":"2015-11-20T21:08:18Z","abstract_excerpt":"Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\\ldots,v_n$, one by one. After seeing each vector $v_i$, we have to output the product $Mv_i$ before we can see the next vector. A naive algorithm can solve this problem using $O(n^3)$ time in total, and its running time can be slightly improved to $O(n^3/\\log^2 n)$ [Williams SODA'07]. We show that a conjecture that there is no truly subcubic ($O(n^{3-\\epsilon})$) time algorithm for this problem can be used to exhibi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06773","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"}