Efficient algorithms for centers and medians in interval and circular-arc graphs

S. Bespamyatnikh, B. Bhattacharya, J. Mark Keil, D. Kirkpatrick, M. Segal

Research output: Contribution to journalArticlepeer-review

Abstract

The p-center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The p-median problem is to locate p facilities on a network so as to minimize the average distance from one of the n demand points to one of the p facilities. We provide, given the interval model of an n vertex interval graph, an Ofn) time algorithm for the 1-median problem on the interval graph. We also show how to solve the p-median problem, for arbitrary p, on an interval graph in 0(pn log n) time and on an circular-arc graph in 0(pn2 logn) time. Other than for trees, no polynomial time algorithm for p-median problem has been reported for any large class of graphs. We introduce a spring model of computation and show how to solve the p-center problem on an circular-arc graph in 0(pn) time, assuming that the arc endpoints are sorted.

Original languageEnglish
Pages (from-to)100-112
Number of pages13
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1879
DOIs
StatePublished - 1 Jan 2000
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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