License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07261.4
URN: urn:nbn:de:0030-drops-12282
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2007/1228/
|
Go to the corresponding Portal |
Levin, Asaf
Approximating min-max k-clustering
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 $(2k-1)$-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
@InProceedings{levin:DagSemProc.07261.4,
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 = {https://drops.dagstuhl.de/opus/volltexte/2007/1228},
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 |
