{"paper":{"title":"Scalable Auction Algorithms for Bipartite Maximum Matching Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Quanquan C. Liu, Samir Khuller, Yiduo Ke","submitted_at":"2023-07-18T05:25:32Z","abstract_excerpt":"In this paper, we give new auction algorithms for maximum weighted bipartite matching (MWM) and maximum cardinality bipartite $b$-matching (MCbM). Our algorithms run in $O\\left(\\log n/\\varepsilon^8\\right)$ and $O\\left(\\log n/\\varepsilon^2\\right)$ rounds, respectively, in the blackboard distributed setting. We show that our MWM algorithm can be implemented in the distributed, interactive setting using $O(\\log^2 n)$ and $O(\\log n)$ bit messages, respectively, directly answering the open question posed by Demange, Gale and Sotomayor [DNO14]. Furthermore, we implement our algorithms in a variety o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08979","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/2307.08979/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"}