The Euclidean k-supplier problem

Viswanath Nagarajan, Baruch Schieber, Hadas Shachnai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

In the k-supplier problem, we are given a set of clients C and set of facilities F located in a metric (C∪F, d), along with a bound k. The goal is to open a subset of k facilities so as to minimize the maximum distance of a client to an open facility, i.e., minS⊆F: |S|=kmax v∈C d(v,S), where d(v,S) = minu∈S d(v,u) is the minimum distance of client v to any facility in S. We present a 1 + √3 < 2.74 approximation algorithm for the k-supplier problem in Euclidean metrics. This improves the previously known 3-approximation algorithm [9] which also holds for general metrics (where it is known to be tight). It is NP-hard to approximate Euclidean k-supplier to better than a factor of √7 ≈ 2.65, even in dimension two [5]. Our algorithm is based on a relation to the edge cover problem. We also present a nearly linear O(n·log2 n) time algorithm for Euclidean k-supplier in constant dimensions that achieves an approximation ratio of 2.965, where n = |C∪F|.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings
Pages290-301
Number of pages12
DOIs
StatePublished - 2013
Externally publishedYes
Event16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 - Valparaiso, Chile
Duration: Mar 18 2013Mar 20 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013
CountryChile
CityValparaiso
Period3/18/133/20/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'The Euclidean k-supplier problem'. Together they form a unique fingerprint.

Cite this