{"title":"基于随机公式的步行分析","authors":"A. Coja-Oghlan, A. Frieze","doi":"10.1137/12090191X","DOIUrl":null,"url":null,"abstract":"Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of Φ in polynomial time w.h.p. if m/n ≤ ρ · 2k/k for a certain constant ρ > 0. This is an improvement by a factor of Θ(k) over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"Analyzing Walksat on Random Formulas\",\"authors\":\"A. Coja-Oghlan, A. Frieze\",\"doi\":\"10.1137/12090191X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of Φ in polynomial time w.h.p. if m/n ≤ ρ · 2k/k for a certain constant ρ > 0. This is an improvement by a factor of Θ(k) over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).\",\"PeriodicalId\":340112,\"journal\":{\"name\":\"Workshop on Analytic Algorithmics and Combinatorics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Workshop on Analytic Algorithmics and Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/12090191X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Workshop on Analytic Algorithmics and Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/12090191X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of Φ in polynomial time w.h.p. if m/n ≤ ρ · 2k/k for a certain constant ρ > 0. This is an improvement by a factor of Θ(k) over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).
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