{"paper":{"title":"Concentration and maximin fair allocations for subadditive valuations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Shengyu Huang, Uriel Feige","submitted_at":"2025-02-19T08:49:57Z","abstract_excerpt":"We consider fair allocation of $m$ indivisible items to $n$ agents of equal entitlements, with submodular valuation functions. Previously, Seddighin and Seddighin [{\\em Artificial Intelligence} 2024] proved the existence of allocations that offer each agent at least a $\\frac{1}{c \\log n \\log\\log n}$ fraction of her maximin share (MMS), where $c$ is some large constant (over 1000, in their work). We modify their algorithm and improve its analysis, improving the ratio to $\\frac{1}{14 \\log n}$.\n  Some of our improvement stems from tighter analysis of concentration properties for the value of any "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13541","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/2502.13541/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"}