{"title":"Approximation Algorithms for Matroid and Knapsack Means Problems","authors":"Ao Zhao, Qian Liu, Yang Zhou, Min Li","doi":"10.1142/s0217595922400073","DOIUrl":null,"url":null,"abstract":"In this paper, we concentrate on studying the [Formula: see text]-means problem with a matroid or a knapsack constraint. In the matroid means problem, given an observation set and a matroid, the goal is to find a center set from the independent sets to minimize the cost. By using the linear programming [Formula: see text]-rounding technology, we obtain a constant approximation guarantee. For the knapsack means problem, we adopt a similar strategy to that of matroid means problem, whereas the difference is that we add a knapsack covering inequality to the relaxed LP in order to decrease the unbounded integrality gap.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asia Pac. J. Oper. Res.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0217595922400073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we concentrate on studying the [Formula: see text]-means problem with a matroid or a knapsack constraint. In the matroid means problem, given an observation set and a matroid, the goal is to find a center set from the independent sets to minimize the cost. By using the linear programming [Formula: see text]-rounding technology, we obtain a constant approximation guarantee. For the knapsack means problem, we adopt a similar strategy to that of matroid means problem, whereas the difference is that we add a knapsack covering inequality to the relaxed LP in order to decrease the unbounded integrality gap.