{"paper":{"title":"The limits of SDP relaxations for general-valued CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Johan Thapper, Stanislav Zivny","submitted_at":"2016-12-04T17:23:42Z","abstract_excerpt":"It has been shown that for a general-valued constraint language $\\Gamma$ the following statements are equivalent: (1) any instance of $\\operatorname{VCSP}(\\Gamma)$ can be solved to optimality using a constant level of the Sherali-Adams LP hierarchy; (2) any instance of $\\operatorname{VCSP}(\\Gamma)$ can be solved to optimality using the third level of the Sherali-Adams LP hierarchy; (3) the support of $\\Gamma$ satisfies the \"bounded width condition\", i.e., it contains weak near-unanimity operations of all arities.\n  We show that if the support of $\\Gamma$ violates the bounded width condition th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01147","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"}