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

✍ Scribed by Sergei Bespamyatnikh; Binay Bhattacharya; Mark Keil; David Kirkpatrick; Michael Segal

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 267 KB
• Volume: 39
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/net.10023

✦ Synopsis

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 a demand point to its closest facility. We consider these problems when the network can be modeled by an interval or circular‐arc graph whose edges have unit lengths. We provide, given the interval model of an n vertex interval graph, an O(n) 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 O(pn log n) time and on a circular‐arc graph in O(pn^2^ log n) time. We introduce a spring representation of the objective function and show how to solve the p‐center problem on a circular‐arc graph in O(pn) time, assuming that the arc endpoints are sorted. © 2002 Wiley Periodicals, Inc.