{"paper":{"title":"Distributed Approximate Maximum Matching and Minimum Vertex Cover via Generalized Graph Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Randomized algorithms achieve 2+ε-approximate maximum matching and approximate weighted minimum vertex cover in O(log n / log² log n) rounds in the LOCAL model.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Peter Davies-Peck","submitted_at":"2026-05-13T09:45:29Z","abstract_excerpt":"The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\\Omega(\\min\\{\\sqrt{\\frac{\\log n}{\\log\\log n}}, \\frac{\\log \\Delta}{\\log\\log \\Delta}\\})$ rounds, for any polylogarithmic or smaller approximation ratio. As a function of $\\Delta$, this complexity was subsequently matched for constant-approximate weighted vertex cover [Bar-Yehuda, Censor-Hillel and Schwartzman, JACM 2017] and constant-approximate maximum matching [Bar-Yehuda, Censor-Hillel, Ghaffari and Sch"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show randomized algorithms for 2+ε-approximate maximum matching and approximate (weighted) minimum vertex cover taking O(log n / log² log n) rounds.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The novel graph decomposition generalizing Miller, Peng and Xu works as claimed to reduce the effective degree of high-degree graphs in the LOCAL model.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Randomized LOCAL-model algorithms achieve 2+ε-approximate maximum matching and approximate minimum vertex cover in O(log n / log² log n) rounds via a generalized graph decomposition, establishing that n-dependent complexity is required.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Randomized algorithms achieve 2+ε-approximate maximum matching and approximate weighted minimum vertex cover in O(log n / log² log n) rounds in the LOCAL model.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"91664b3890cefacf4aced56d95d9fe3e9ac1b093ec7a27209d890cdccd6ab5a0"},"source":{"id":"2605.13264","kind":"arxiv","version":1},"verdict":{"id":"0f44f64b-cb96-464a-8218-d83ed0f5468d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:54:30.384808Z","strongest_claim":"We show randomized algorithms for 2+ε-approximate maximum matching and approximate (weighted) minimum vertex cover taking O(log n / log² log n) rounds.","one_line_summary":"Randomized LOCAL-model algorithms achieve 2+ε-approximate maximum matching and approximate minimum vertex cover in O(log n / log² log n) rounds via a generalized graph decomposition, establishing that n-dependent complexity is required.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The novel graph decomposition generalizing Miller, Peng and Xu works as claimed to reduce the effective degree of high-degree graphs in the LOCAL model.","pith_extraction_headline":"Randomized algorithms achieve 2+ε-approximate maximum matching and approximate weighted minimum vertex cover in O(log n / log² log n) rounds in the LOCAL model."},"references":{"count":23,"sample":[{"doi":"","year":1989,"title":"B. Awerbuch, M. Luby, A.V. Goldberg, and S.A. Plotkin. Network decomposition and locality in distributed computation. 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