{"paper":{"title":"On the Assadi Liu Tarjan Auction Algorithm for Bipartite Matching: Simplification, Alternative Analysis, and Hard Instance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Archie Walton, Christian Konrad, Eric Wang, Kheeran K. Naidu","submitted_at":"2026-07-08T14:11:13Z","abstract_excerpt":"Assadi, Liu, and Tarjan [SOSA'21] gave an auction algorithm that outputs a $(1-\\epsilon)$-approximation to Maximum Matching in bipartite graphs. Their algorithm computes a sequence of $O(\\frac{1}{\\epsilon^2})$ maximal matchings in subgraphs of the input graph and can be implemented in the multi-pass streaming setting with $O(\\frac{1}{\\epsilon^2})$ passes in a straightforward manner, which constitutes the state-of-the-art pass/approximation trade-off result in the multi-pass streaming setting. Their analysis uses tools from combinatorial auctions and, at its heart, relies on a clever potential "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07439","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/2607.07439/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"}