Levin, Asaf
Approximating minmax kclustering
Abstract
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 $(2k1)$approximation algorithm for $kgeq 3$, a
2approximation algorithm for $k=2$, and we also show a lower
bound of $k$ on the performance guarantee of any
polynomialtime algorithm.
We then consider special cases of this problem arising in vehicle routing problems, and present improved results.
BibTeX  Entry
@InProceedings{levin:DSP:2007:1228,
author = {Asaf Levin},
title = {Approximating minmax kclustering},
booktitle = {Fair Division},
year = {2007},
editor = {Steven Brams and Kirk Pruhs and Gerhard Woeginger},
number = {07261},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2007/1228},
annote = {Keywords: Approximation algorithms}
}
Keywords: 

Approximation algorithms 
Seminar: 

07261  Fair Division

Issue date: 

2007 
Date of publication: 

26.11.2007 