{"paper":{"title":"On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"Euiwoong Lee, Ian DeHaan, Neng Huang","submitted_at":"2025-07-11T15:46:31Z","abstract_excerpt":"We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language $\\Gamma$ which has the dual discriminator operation as a polymorphism, there exists a $|D|$-approximation algorithm for MinCostCSP$(\\Gamma)$ where $D$ is the domain. Complementing our algorithmic result, we show that any constraint language $\\Gamma$ where MinCostCSP$(\\Gamma)$ admits a constant-factor approximation must have a \\emph{near-unanimity} (NU) polymorphism unless P = NP, extending a similar result by Dalmau et al. on MinCSPs. These results imply a di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08693","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08693/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"}