{"title":"约束子模最大化:超过1/e","authors":"Alina Ene, Huy L. Nguyen","doi":"10.1109/FOCS.2016.34","DOIUrl":null,"url":null,"abstract":"In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm [Feldman et al., FOCS 2011].","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"78","resultStr":"{\"title\":\"Constrained Submodular Maximization: Beyond 1/e\",\"authors\":\"Alina Ene, Huy L. Nguyen\",\"doi\":\"10.1109/FOCS.2016.34\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm [Feldman et al., FOCS 2011].\",\"PeriodicalId\":414001,\"journal\":{\"name\":\"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"78\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FOCS.2016.34\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FOCS.2016.34","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 78
摘要
在这项工作中，我们提出了一种新的算法来最大化受一般约束的非单调子模函数。我们的算法找到了函数在下闭多面体上的多线性扩展最大化的近似分数解。近似保证为0.372，这是对统一连续贪婪算法实现的1/e近似的第一次改进[Feldman et al.， FOCS 2011]。
In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm [Feldman et al., FOCS 2011].
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