{"paper":{"title":"On Approximate Fully-Dynamic Matching and Online Matrix-Vector Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Yang P. Liu","submitted_at":"2024-03-05T01:33:09Z","abstract_excerpt":"We study connections between the problem of fully dynamic $(1-\\epsilon)$-approximate maximum bipartite matching, and the dual $(1+\\epsilon)$-approximate vertex cover problem, with the online matrix-vector ($\\mathsf{OMv}$) conjecture which has recently been used in several fine-grained hardness reductions. We prove that there is an online algorithm that maintains a $(1+\\epsilon)$-approximate vertex cover in amortized $n^{1-c}\\epsilon^{-C}$ time for constants $c, C > 0$ for fully dynamic updates if and only if the $\\mathsf{OMv}$ conjecture is false. Similarly, we prove that there is an online al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.02582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.02582/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}