{"paper":{"title":"Almost Tight Bounds for Online Hypergraph Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Rajan Udwani, Thorben Tr\\\"obst","submitted_at":"2024-02-13T20:17:24Z","abstract_excerpt":"In the online hypergraph matching problem, hyperedges of size $k$ over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A na\\\"ive greedy algorithm for this problem achieves a competitive ratio of $\\frac{1}{k}$. We show that no (randomized) online algorithm has competitive ratio better than $\\frac{2+o(1)}{k}$. If edges are allowed to be assigned fractionally, we give a deterministic online algorithm with competitive ratio $\\frac{1-o(1)}{\\ln(k)}$ and show that no online algorithm can have competitive ratio strictly bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.08775","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/2402.08775/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"}