{"paper":{"title":"Maximizing Nash Social Welfare in 2-Value Instances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Bhaskar Ray Chaudhury, Ernest van Wijland, Giovanna Varricchio, Golnoosh Shahkarami, Hannaneh Akrami, Kurt Mehlhorn, Marco Schmalhofer, Martin Hoefer, Quentin Vermande","submitted_at":"2021-07-19T15:27:04Z","abstract_excerpt":"We consider the problem of maximizing the Nash social welfare when allocating a set $\\mathcal{G}$ of indivisible goods to a set $\\mathcal{N}$ of agents. We study instances, in which all agents have 2-value additive valuations: The value of every agent $i \\in \\mathcal{N}$ for every good $j \\in \\mathcal{G}$ is $v_{ij} \\in \\{p,q\\}$, for $p,q \\in \\mathbb{N}$, $p \\le q$. Maybe surprisingly, we design an algorithm to compute an optimal allocation in polynomial time if $p$ divides $q$, i.e., when $p=1$ and $q \\in \\mathbb{N}$ after appropriate scaling. The problem is \\classNP-hard whenever $p$ and $q$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08965","kind":"arxiv","version":2},"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/2107.08965/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"}