License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.57
URN: urn:nbn:de:0030-drops-126609
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12660/
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Gamlath, Buddhima ; Grinberg, Vadim

Approximating Star Cover Problems

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LIPIcs-APPROX57.pdf (0.6 MB)

Abstract

Given a metric space (F ∪ C, d), we consider star covers of C with balanced loads. A star is a pair (i, C_i) where i ∈ F and C_i ⊆ C, and the load of a star is ∑_{j ∈ 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.

BibTeX - Entry

@InProceedings{gamlath_et_al:LIPIcs:2020:12660,
  author =	{Buddhima Gamlath and Vadim Grinberg},
  title =	{{Approximating Star Cover Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12660},
  URN =		{urn:nbn:de:0030-drops-126609},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.57},
  annote =	{Keywords: star cover, approximation algorithms, lp rounding}
}

Keywords: star cover, approximation algorithms, lp rounding
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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