When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07261.4
URN: urn:nbn:de:0030-drops-12282
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Levin, Asaf

Approximating min-max k-clustering

07261.LevinAsaf.ExtAbstract.1228.pdf (0.09 MB)


We consider the
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 =	{Levin, Asaf},
  title =	{{Approximating min-max k-clustering}},
  booktitle =	{Fair Division},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-12282},
  doi =		{10.4230/DagSemProc.07261.4},
  annote =	{Keywords: Approximation algorithms}

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

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