{"paper":{"title":"Sub-exponential Approximation Schemes for CSPs: from Dense to Almost Sparse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dimitris Fotakis, Michael Lampis, Vangelis Th. Paschos","submitted_at":"2015-07-15T20:48:19Z","abstract_excerpt":"It has long been known, since the classical work of (Arora, Karger, Karpinski, JCSS~99), that \\MC\\ admits a PTAS on dense graphs, and more generally, \\kCSP\\ admits a PTAS on \"dense\" instances with $\\Omega(n^k)$ constraints. In this paper we extend and generalize their exhaustive sampling approach, presenting a framework for $(1-\\eps)$-approximating any \\kCSP\\ problem in \\emph{sub-exponential} time while significantly relaxing the denseness requirement on the input instance. Specifically, we prove that for any constants $\\delta \\in (0, 1]$ and $\\eps > 0$, we can approximate \\kCSP\\ problems with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04391","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"}