LP Rounding for k-Centers with Non-uniform Hard Capacities release_5esduijwuzc4bfdsjzwg4cicpa

by Marek Cygan, MohammadTaghi Hajiaghayi, Samir Khuller

Released as a article .

2012  

Abstract

In this paper we consider a generalization of the classical k-center problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The objective is to minimize the maximum distance a node has to travel to get to its assigned center. This problem is NP-hard, even when centers have no capacity restrictions and optimal factor 2 approximation algorithms are known. With capacities, when all centers have identical capacities, a 6 approximation is known with no better lower bounds than for the infinite capacity version. While many generalizations and variations of this problem have been studied extensively, no progress was made on the capacitated version for a general capacity function. We develop the first constant factor approximation algorithm for this problem. Our algorithm uses an LP rounding approach to solve this problem, and works for the case of non-uniform hard capacities, when multiple copies of a node may not be chosen and can be extended to the case when there is a hard bound on the number of copies of a node that may be selected. In addition we establish a lower bound on the integrality gap of 7(5) for non-uniform (uniform) hard capacities. In addition we prove that if there is a (3-eps)-factor approximation for this problem then P=NP. Finally, for non-uniform soft capacities we present a much simpler 11-approximation algorithm, which we find as one more evidence that hard capacities are much harder to deal with.
In text/plain format

Archived Files and Locations

application/pdf  517.4 kB
file_wzegpnxv4vgzbcs7rftavrmgeq
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2012-08-15
Version   v1
Language   en ?
arXiv  1208.3054v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: ceb8a594-e535-444a-86a2-42a8aacadbfc
API URL: JSON