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.ESA.2020.9
URN: urn:nbn:de:0030-drops-128759
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12875/
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Bandyapadhyay, Sayan

Improved Bounds for Metric Capacitated Covering Problems

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LIPIcs-ESA-2020-9.pdf (0.4 MB)

Abstract

In the Metric Capacitated Covering (MCC) problem, given a set of balls ℬ in a metric space P with metric d and a capacity parameter U, the goal is to find a minimum sized subset ℬ' ⊆ ℬ and an assignment of the points in P to the balls in ℬ' such that each point is assigned to a ball that contains it and each ball is assigned with at most U points. MCC achieves an O(log |P|)-approximation using a greedy algorithm. On the other hand, it is hard to approximate within a factor of o(log |P|) even with β < 3 factor expansion of the balls. Bandyapadhyay et al. [SoCG 2018, DCG 2019] showed that one can obtain an O(1)-approximation for the problem with 6.47 factor expansion of the balls. An open question left by their work is to reduce the gap between the lower bound 3 and the upper bound 6.47. In this current work, we show that it is possible to obtain an O(1)-approximation with only 4.24 factor expansion of the balls. We also show a similar upper bound of 5 for a more generalized version of MCC for which the best previously known bound was 9.

BibTeX - Entry

@InProceedings{bandyapadhyay:LIPIcs:2020:12875,
  author =	{Sayan Bandyapadhyay},
  title =	{{Improved Bounds for Metric Capacitated Covering Problems}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12875},
  URN =		{urn:nbn:de:0030-drops-128759},
  doi =		{10.4230/LIPIcs.ESA.2020.9},
  annote =	{Keywords: Capacitated covering, approximation algorithms, bicriteria approximation, LP rounding}
}

Keywords: Capacitated covering, approximation algorithms, bicriteria approximation, LP rounding
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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