{"paper":{"title":"Faster and Simpler Sketches of Valuation Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.GT","authors_text":"Keren Cohavi, Shahar Dobzinski","submitted_at":"2014-07-27T18:15:23Z","abstract_excerpt":"We present fast algorithms for sketching valuation functions. Let $N$ ($|N|=n$) be some ground set and $v:2^N\\rightarrow \\mathbb R$ be a function. We say that $\\tilde v:2^N\\rightarrow \\mathbb R$ is an $\\alpha$-sketch of $v$ if for every set $S$ we have that $\\frac {v(S)} {\\alpha} \\leq \\tilde v(S) \\leq v(S)$ and $\\tilde v$ can be described in $poly(n)$ bits.\n  Goemans et al. [SODA'09] showed that if $v$ is submodular then there exists an $\\tilde O(\\sqrt n)$-sketch that can be constructed using polynomially many value queries (this is the best possible, as Balcan and Harvey [STOC'11] show that n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7269","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"}