{"title":"绕过KLS:高斯冷却和O^*(n3)体积算法","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":"{\"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}","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}
Bypassing KLS: Gaussian Cooling and an O^*(n3) Volume Algorithm
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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