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  • 标题:Approximating Star Cover Problems
  • 本地全文:下载
  • 作者:Buddhima Gamlath ; Vadim Grinberg
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2020
  • 卷号:176
  • 页码:57:1-57:19
  • DOI:10.4230/LIPIcs.APPROX/RANDOM.2020.57
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Given a metric space (F â^ª C, d), we consider star covers of C with balanced loads. A star is a pair (i, C_i) where i â^^ F and C_i âS† C, and the load of a star is â^'_{j â^^ C_i} d(i, j). In minimum load k-star cover problem (MLkSC), one tries to cover the set of clients C using k stars that minimize the maximum load of a star, and in minimum size star cover (MSSC) one aims to find the minimum number of stars of load at most T needed to cover C, where T is a given parameter. We obtain new bicriteria approximations for the two problems using novel rounding algorithms for their standard LP relaxations. For MLkSC, we find a star cover with (1+O(ε))k stars and O(1/ε²)OPT_MLk load where OPT_MLk is the optimum load. For MSSC, we find a star cover with O(1/ε²) OPT_MS stars of load at most (2 + O(ε)) T where OPT_MS is the optimal number of stars for the problem. Previously, non-trivial bicriteria approximations were known only when F = C.
  • 关键词:star cover; approximation algorithms; lp rounding
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