when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-12282

Levin, Asaf

Approximating min-max k-clustering

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We consider the problems of set partitioning into $k$ clusters with minimum of the maximum cost of a cluster. The cost function is given by an oracle, and we assume that it satisfies some natural structural constraints. That is, we assume that the cost function is monotone, the cost of a singleton is zero, and we assume that for all $S cap S' eq emptyset$ the following holds $c(S) + c(S') geq c(S cup S')$. For this problem we present a $(2k-1)$-approximation algorithm for $kgeq 3$, a 2-approximation algorithm for $k=2$, and we also show a lower bound of $k$ on the performance guarantee of any polynomial-time algorithm. We then consider special cases of this problem arising in vehicle routing problems, and present improved results.

BibTeX - Entry

  author =	{Asaf Levin},
  title =	{Approximating min-max k-clustering},
  booktitle =	{Fair Division},
  year =	{2007},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  number =	{07261},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Approximation algorithms}

Keywords: Approximation algorithms
Seminar: 07261 - Fair Division
Issue date: 2007
Date of publication: 26.11.2007

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