{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8190","name":"Improved Exact Algorithms for Mildly Sparse Instances of Max SAT","abstract":"We present improved exponential time exact algorithms for Max SAT. Our algorithms run in time of the form O(2^{(1-mu(c))n}) for instances with n variables and m=cn clauses. In this setting, there are three incomparable currently best algorithms: a deterministic exponential space algorithm with mu(c)=1\/O(c * log(c)) due to Dantsin and Wolpert [SAT 2006], a randomized polynomial space algorithm with mu(c)=1\/O(c * log^3(c)) and a deterministic polynomial space algorithm with mu(c)=1\/O(c^2 * log^2(c)) due to Sakai, Seto and Tamaki [Theory Comput. Syst., 2015]. Our first result is a deterministic polynomial space algorithm with mu(c)=1\/O(c * log(c)) that achieves the previous best time complexity without exponential space or randomization. Furthermore, this algorithm can handle instances with exponentially large weights and hard constraints. The previous algorithms and our deterministic polynomial space algorithm run super-polynomially faster than 2^n only if m=O(n^2).\r\n\r\nOur second results are deterministic exponential space algorithms for Max SAT with mu(c)=1\/O((c * log(c))^{2\/3}) and for Max 3-SAT with mu(c)=1\/O(c^{1\/2}) that run super-polynomially faster than 2^n when m=o(n^{5\/2}\/log^{5\/2}(n)) and m=o(n^3\/log^2(n)) respectively.","keywords":["maximum satisfiability","weighted","polynomial space","exponential space"],"author":[{"@type":"Person","name":"Sakai, Takayuki","givenName":"Takayuki","familyName":"Sakai"},{"@type":"Person","name":"Seto, Kazuhisa","givenName":"Kazuhisa","familyName":"Seto"},{"@type":"Person","name":"Tamaki, Suguru","givenName":"Suguru","familyName":"Tamaki"},{"@type":"Person","name":"Teruyama, Junichi","givenName":"Junichi","familyName":"Teruyama"}],"position":8,"pageStart":90,"pageEnd":101,"dateCreated":"2015-11-19","datePublished":"2015-11-19","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Sakai, Takayuki","givenName":"Takayuki","familyName":"Sakai"},{"@type":"Person","name":"Seto, Kazuhisa","givenName":"Kazuhisa","familyName":"Seto"},{"@type":"Person","name":"Tamaki, Suguru","givenName":"Suguru","familyName":"Tamaki"},{"@type":"Person","name":"Teruyama, Junichi","givenName":"Junichi","familyName":"Teruyama"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.IPEC.2015.90","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6246","volumeNumber":43,"name":"10th International Symposium on Parameterized and Exact Computation (IPEC 2015)","dateCreated":"2015-11-19","datePublished":"2015-11-19","editor":[{"@type":"Person","name":"Husfeldt, Thore","givenName":"Thore","familyName":"Husfeldt"},{"@type":"Person","name":"Kanj, Iyad","givenName":"Iyad","familyName":"Kanj"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8190","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6246"}}}