Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Levin, Asaf License: Creative Commons Attribution 4.0 license (CC BY 4.0)
when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-12282

Approximating min-max k-clustering



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

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI