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European Symposium on Algorithms

ESA 2000: Algorithms - ESA 2000 pp 100–112Cite as

Efficient Algorithms for Centers and Medians in Interval and Circular-Arc Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1879))

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 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 an circular sarc graph in O(pn 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 O(pn) time, assuming that the arc endpoints are sorted.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of British Columbia, Vancouver, B.C., Canada, V6T 1Z4

    S. Bespamyatnikh, D. Kirkpatrick & M. Segal

  2. School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6

    B. Bhattacharya

  3. Dept. of Computer Science, University of Saskatchewan, 57 Campus Dr., Saskatoon, Sask, Canada, S7N 5A9

    J. Mark Keil

Authors
  1. S. Bespamyatnikh
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  2. B. Bhattacharya
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  3. J. Mark Keil
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  4. D. Kirkpatrick
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  5. M. Segal
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Mike S. Paterson

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© 2000 Springer-Verlag Berlin Heidelberg

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Bespamyatnikh, S., Bhattacharya, B., Keil, J.M., Kirkpatrick, D., Segal, M. (2000). Efficient Algorithms for Centers and Medians in Interval and Circular-Arc Graphs. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_10

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  • DOI: https://doi.org/10.1007/3-540-45253-2_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41004-1

  • Online ISBN: 978-3-540-45253-9

  • eBook Packages: Springer Book Archive

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