eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-11-26
1
5
10.4230/DagSemProc.07261.4
article
Approximating min-max k-clustering
Levin, Asaf
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol07261/DagSemProc.07261.4/DagSemProc.07261.4.pdf
Approximation algorithms