{"paper":{"title":"On the Approximability of Boolean Max-$k$-CSP","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Ainesh Bakshi","submitted_at":"2026-08-05T18:41:43Z","abstract_excerpt":"Consider the problem of maximizing the number of satisfied constraints of an arbitrary boolean constraint satisfaction problem with arity $k$. We obtain a polynomial time algorithm that achieves a $(k/2^k)$-approximation, improving on the previous best guarantee of $0.626612\\; k/2^k$, due to Makarychev and Makarychev (arXiv:1206.3603). Assuming the Unique Games Conjecture, De and Mossel (arXiv:1202.5258) showed that achieving an approximation ratio better than $(k+1)/2^k$ for odd $k$ and $(k+2)/2^k$ for even $k$, is NP-hard. The main technical ingredient is an extension of a recently establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05331","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/2608.05331/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"}