{"paper":{"title":"On the Hardness of Welfare Maximization in Combinatorial Auctions with Submodular Valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DS","authors_text":"Jan Vondrak, Shahar Dobzinski","submitted_at":"2012-02-13T17:09:58Z","abstract_excerpt":"We present a new type of monotone submodular functions: \\emph{multi-peak submodular functions}. Roughly speaking, given a family of sets $\\cF$, we construct a monotone submodular function $f$ with a high value $f(S)$ for every set $S \\in {\\cF}$ (a \"peak\"), and a low value on every set that does not intersect significantly any set in $\\cF$.\n  We use this construction to show that a better than $(1-\\frac{1}{2e})$-approximation ($\\simeq 0.816$) for welfare maximization in combinatorial auctions with submodular valuations is (1) impossible in the communication model, (2) NP-hard in the computation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2792","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":""},"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"}