{"paper":{"title":"Deterministic Dynamic Maximal Matching in Sublinear Update Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aaron Bernstein, Peter Kiss, Sayan Bhattacharya, Thatchaphol Saranurak","submitted_at":"2025-04-29T13:59:33Z","abstract_excerpt":"We give a fully dynamic deterministic algorithm for maintaining a maximal matching of an $n$-vertex graph in $\\tilde{O}(n^{8/9})$ amortized update time. This breaks the long-standing $\\Omega(n)$-update-time barrier on dense graphs, achievable by trivially scanning all incident vertices of the updated edge, and affirmatively answers a major open question repeatedly asked in the literature [BGS15, BCHN18, Sol22]. We also present a faster randomized algorithm against an adaptive adversary with $\\tilde{O}(n^{3/4})$ amortized update time.\n  Our approach employs the edge degree constrained subgraph "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20780","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/2504.20780/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"}