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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.57
URN: urn:nbn:de:0030-drops-126609
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12660/
Gamlath, Buddhima ; Grinberg, Vadim
Approximating Star Cover Problems
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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 | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 11.08.2020 |
