{"title":"Bypassing KLS: Gaussian Cooling and an O^*(n3) Volume Algorithm","authors":"Benjamin R. Cousins, S. Vempala","doi":"10.1145/2746539.2746563","DOIUrl":null,"url":null,"abstract":"We present an O*(n3) randomized algorithm for estimating the volume of a well-rounded convex body given by a membership oracle, improving on the previous best complexity of O*(n4). The new algorithmic ingredient is an accelerated cooling schedule where the rate of cooling increases with the temperature. Previously, the known approach for potentially achieving such complexity relied on a positive resolution of the KLS hyperplane conjecture, a central open problem in convex geometry.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"70 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"54","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2746539.2746563","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 54
Abstract
We present an O*(n3) randomized algorithm for estimating the volume of a well-rounded convex body given by a membership oracle, improving on the previous best complexity of O*(n4). The new algorithmic ingredient is an accelerated cooling schedule where the rate of cooling increases with the temperature. Previously, the known approach for potentially achieving such complexity relied on a positive resolution of the KLS hyperplane conjecture, a central open problem in convex geometry.
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