{"title":"提升和旋转，以提高加权完成时间在不相关的机器","authors":"N. Bansal, O. Svensson, A. Srinivasan","doi":"10.1145/2897518.2897572","DOIUrl":null,"url":null,"abstract":"We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a (3/2-c)-approximation algorithm for some fixed c>0, improving upon the long-standing bound of 3/2. To do this, we first introduce a new lift-and-project based SDP relaxation for the problem. This is necessary as the previous convex programming relaxations have an integrality gap of 3/2. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.","PeriodicalId":442965,"journal":{"name":"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"40","resultStr":"{\"title\":\"Lift-and-round to improve weighted completion time on unrelated machines\",\"authors\":\"N. Bansal, O. Svensson, A. Srinivasan\",\"doi\":\"10.1145/2897518.2897572\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a (3/2-c)-approximation algorithm for some fixed c>0, improving upon the long-standing bound of 3/2. To do this, we first introduce a new lift-and-project based SDP relaxation for the problem. This is necessary as the previous convex programming relaxations have an integrality gap of 3/2. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.\",\"PeriodicalId\":442965,\"journal\":{\"name\":\"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"40\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2897518.2897572\",\"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-eighth annual ACM symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2897518.2897572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lift-and-round to improve weighted completion time on unrelated machines
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a (3/2-c)-approximation algorithm for some fixed c>0, improving upon the long-standing bound of 3/2. To do this, we first introduce a new lift-and-project based SDP relaxation for the problem. This is necessary as the previous convex programming relaxations have an integrality gap of 3/2. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.
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