Albert Atserias, Ilario Bonacina, Susanna F. de Rezende, Massimo Lauria, Jakob Nordström, A. Razborov
{"title":"Clique is hard on average for regular resolution","authors":"Albert Atserias, Ilario Bonacina, Susanna F. de Rezende, Massimo Lauria, Jakob Nordström, A. Razborov","doi":"10.1145/3188745.3188856","DOIUrl":null,"url":null,"abstract":"We prove that for k ≪ n1/4 regular resolution requires length nΩ(k) to establish that an Erdos-Renyi graph with appropriately chosen edge density does not contain a k-clique. This lower bound is optimal up to the multiplicative constant in the exponent, and also implies unconditional nΩ(k) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.","PeriodicalId":20593,"journal":{"name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","volume":"98 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3188745.3188856","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 20
Abstract
We prove that for k ≪ n1/4 regular resolution requires length nΩ(k) to establish that an Erdos-Renyi graph with appropriately chosen edge density does not contain a k-clique. This lower bound is optimal up to the multiplicative constant in the exponent, and also implies unconditional nΩ(k) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.
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