{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T04:11:39Z","timestamp":1687320699580},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Science Foundation","award":["1764385"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"We show that for every $r \\ge 2$ there exists $\\epsilon_r > 0$ such that any\n$r$-uniform hypergraph with $m$ edges and maximum vertex degree $o(\\sqrt{m})$\ncontains a set of at most $(\\frac{1}{2} - \\epsilon_r)m$ edges the removal of\nwhich breaks the hypergraph into connected components with at most $m\/2$ edges.\nWe use this to give an algorithm running in time $d^{(1 - \\epsilon_r)m}$ that\ndecides satisfiability of $m$-variable $(d, k)$-CSPs in which every variable\nappears in at most $r$ constraints, where $\\epsilon_r$ depends only on $r$ and\n$k\\in o(\\sqrt{m})$. Furthermore our algorithm solves the corresponding #CSP-SAT\nand Max-CSP-SAT of these CSPs. We also show that CNF representations of\nunsatisfiable $(2, k)$-CSPs with variable frequency $r$ can be refuted in\ntree-like resolution in size $2^{(1 - \\epsilon_r)m}$. Furthermore for Tseitin\nformulas on graphs with degree at most $k$ (which are $(2, k)$-CSPs) we give a\ndeterministic algorithm finding such a refutation.<\/jats:p>","DOI":"10.46298\/lmcs-17(4:17)2021","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T20:19:36Z","timestamp":1639513176000},"source":"Crossref","is-referenced-by-count":0,"title":["A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm"],"prefix":"10.46298","volume":"Volume 17, Issue 4","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-0808-2269","authenticated-orcid":false,"given":"Michal","family":"Kouck\u00fd","sequence":"first","affiliation":[]},{"given":"Vojt\u011bch","family":"R\u00f6dl","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3524-9282","authenticated-orcid":false,"given":"Navid","family":"Talebanfard","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2021,12,13]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/8832\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/8832\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:20:01Z","timestamp":1687292401000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,13]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-17(4:17)2021","relation":{"has-preprint":[{"id-type":"arxiv","id":"2105.06744v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2105.06744v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2105.06744","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2105.06744","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,13]]}}}