When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2008.1315
URN: urn:nbn:de:0030-drops-13156
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Mestre, Julián

Lagrangian Relaxation and Partial Cover (Extended Abstract)

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Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) $alpha$-approximation as a black box can yield an approximation factor better than~$frac{4}{3} alpha$. This matches the upper bound given by K"onemann et al. (ESA 2006, pages 468--479). Faced with this limitation we study a specific, yet broad class of covering problems: Partial Totally Balanced Cover. By carefully analyzing the inner workings of the LMP algorithm we are able to give an almost tight characterization of the integrality gap of the standard linear relaxation of the problem. As a consequence we obtain improved approximations for the Partial version of Multicut and Path Hitting on Trees, Rectangle Stabbing, and Set Cover with $ ho$-Blocks.

BibTeX - Entry

  author =	{Juli{\'a}n Mestre},
  title =	{{Lagrangian Relaxation and Partial Cover (Extended Abstract)}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{539--550},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-13156},
  doi =		{},
  annote =	{Keywords: Lagrangian Relaxation, Partial Cover, Primal-Dual Algorithms}

Keywords: Lagrangian Relaxation, Partial Cover, Primal-Dual Algorithms
Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008

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