{"paper":{"title":"Stochastic Matching via Local Sparsification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Local sparsification guided by fractional solutions preserves the expected size of the maximum matching when spread is sufficient.","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Edith Cohen, Mohammad Roghani, Sara Ahmadian","submitted_at":"2026-05-13T23:25:15Z","abstract_excerpt":"The classic online stochastic matching problem typically requires immediate and irrevocable matching decisions. However, in many modern decentralized systems such as real-time ride-hailing and distributed cloud computing, the primary bottleneck is often local communication bandwidth rather than the timing of the match itself. We formalize this challenge by introducing a two-stage local sparsification framework. In this setting, arriving requests must prune their realized compatibility sets to a strict budget of $k$ edges before a central coordinator optimizes the global matching. This creates "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that under sufficient spread, our sparsifier globally preserves the expected size of the maximum matching.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The fractional solution of the expected instance must exhibit sufficient spread; the paper does not specify how this spread is guaranteed or measured in practice when the instance is unknown in advance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A local selection rule based on a fractional solution of the expected instance preserves the expected maximum matching size under sufficient spread and yields near-optimal global matchings with small local budgets on ride-hailing data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Local sparsification guided by fractional solutions preserves the expected size of the maximum matching when spread is sufficient.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b40d5f4140954abebfe5c712623688730074d1fbd0ffdb9a1e4dd8f5f2d3f39c"},"source":{"id":"2605.14195","kind":"arxiv","version":1},"verdict":{"id":"57b49e50-00f9-469e-add5-c114952d0e7f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:33:02.709866Z","strongest_claim":"We prove that under sufficient spread, our sparsifier globally preserves the expected size of the maximum matching.","one_line_summary":"A local selection rule based on a fractional solution of the expected instance preserves the expected maximum matching size under sufficient spread and yields near-optimal global matchings with small local budgets on ride-hailing data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The fractional solution of the expected instance must exhibit sufficient spread; the paper does not specify how this spread is guaranteed or measured in practice when the instance is unknown in advance.","pith_extraction_headline":"Local sparsification guided by fractional solutions preserves the expected size of the maximum matching when spread is sufficient."},"references":{"count":39,"sample":[{"doi":"10.1002/rsa.3240060107","year":1995,"title":"Jonathan Aronson, Martin E. Dyer, Alan M. Frieze, and Stephen Suen. Randomized greedy matching II.Random Struct. Algorithms, 6(1):55–74, 1995. doi: 10.1002/RSA.3240060107. 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