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.ISAAC.2016.40
URN: urn:nbn:de:0030-drops-68102
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6810/
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Kao, Mong-Jen ; Tu, Hai-Lun ; Lee, D. T.

O(f) Bi-Approximation for Capacitated Covering with Hard Capacities

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Abstract

We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = (V, E) with a maximum edge size f. Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the demands of the edges can be covered by the capacities of the vertices and the multiplicity of each vertex does not exceed its available multiplicity.

In this paper we present an O(f) bi-approximation for VC-HC that gives a trade-off on the number of augmented multiplicity and the cost of the resulting cover. In particular, we show that, by augmenting the available multiplicity by a factor of k geq 2, a cover with a cost ratio of (1+ frac{1}{k - 1})(f - 1) to the optimal cover for the original instance can be obtained. This improves over a previous result, which has a cost ratio of f^2 via augmenting the available multiplicity by a factor of f.

BibTeX - Entry

@InProceedings{kao_et_al:LIPIcs:2016:6810,
  author =	{Mong-Jen Kao and Hai-Lun Tu and D. T. Lee},
  title =	{{O(f) Bi-Approximation for Capacitated Covering with Hard Capacities}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{40:1--40:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6810},
  URN =		{urn:nbn:de:0030-drops-68102},
  doi =		{10.4230/LIPIcs.ISAAC.2016.40},
  annote =	{Keywords: Capacitated Covering, Hard Capacities, Bi-criteria Approximation}
}

Keywords: Capacitated Covering, Hard Capacities, Bi-criteria Approximation
Collection: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 07.12.2016

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