{"paper":{"title":"Incremental $(1-\\epsilon)$-approximate dynamic matching in $O(poly(1/\\epsilon))$ update time","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Joakim Blikstad, Peter Kiss","submitted_at":"2023-02-16T17:10:18Z","abstract_excerpt":"In the dynamic approximate maximum bipartite matching problem we are given bipartite graph $G$ undergoing updates and our goal is to maintain a matching of $G$ which is large compared the maximum matching size $\\mu(G)$. We define a dynamic matching algorithm to be $\\alpha$ (respectively $(\\alpha, \\beta)$)-approximate if it maintains matching $M$ such that at all times $|M | \\geq \\mu(G) \\cdot \\alpha$ (respectively $|M| \\geq \\mu(G) \\cdot \\alpha - \\beta$).\n  We present the first deterministic $(1-\\epsilon )$-approximate dynamic matching algorithm with $O(poly(\\epsilon ^{-1}))$ amortized update ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08432","kind":"arxiv","version":2},"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/2302.08432/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"}