{"paper":{"title":"The power of linear programming for general-valued CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Johan Thapper, Stanislav Zivny, Vladimir Kolmogorov","submitted_at":"2013-11-17T21:37:51Z","abstract_excerpt":"Let $D$, called the domain, be a fixed finite set and let $\\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\\to\\mathbb{Q}\\cup\\{\\infty\\}$, where different functions might have different arity $m$. We study the valued constraint satisfaction problem parametrised by $\\Gamma$, denoted by VCSP$(\\Gamma)$. These are minimisation problems given by $n$ variables and the objective function given by a sum of functions from $\\Gamma$, each depending on a subset of the $n$ variables. Finite-valued constraint languages contain functions that take on only rational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4219","kind":"arxiv","version":3},"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"}