{"title":"随机k-TSP的近似算法","authors":"Alina Ene, V. Nagarajan, Rishi Saket","doi":"10.4230/LIPIcs.FSTTCS.2017.27","DOIUrl":null,"url":null,"abstract":"We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\\log k)$-approximation algorithm, and a non-adaptive $O(\\log^2k)$-approximation algorithm. We also show that the adaptivity gap of this problem is between $e$ and $O(\\log^2k)$.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Approximation Algorithms for Stochastic k-TSP\",\"authors\":\"Alina Ene, V. Nagarajan, Rishi Saket\",\"doi\":\"10.4230/LIPIcs.FSTTCS.2017.27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\\\\log k)$-approximation algorithm, and a non-adaptive $O(\\\\log^2k)$-approximation algorithm. We also show that the adaptivity gap of this problem is between $e$ and $O(\\\\log^2k)$.\",\"PeriodicalId\":175000,\"journal\":{\"name\":\"Foundations of Software Technology and Theoretical Computer Science\",\"volume\":\"60 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations of Software Technology and Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.FSTTCS.2017.27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Software Technology and Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.FSTTCS.2017.27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\log k)$-approximation algorithm, and a non-adaptive $O(\log^2k)$-approximation algorithm. We also show that the adaptivity gap of this problem is between $e$ and $O(\log^2k)$.
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