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k-Center

  • Vijay V. Vazirani

Abstract

Consider the following application. Given a set of cities, with intercity distances specified, pick k cities for locating warehouses in so as to minimize the maximum distance of a city from its closest warehouse. We will study this problem, called the k-center problem, and its weighted version, under the restriction that the edge costs satisfy the triangle inequality. Without this restriction, the k-center problem cannot be approximated within factor α(n), for any computable function α(n), assuming PNP (see Exercise 5.1).

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Notes

  1. 134.
    D.S. Hochbaum and D.B. Shmoys. A unified approach to approximation algorithms for bottleneck problems. Journal of the ACM, 33: 533–550, 1986.MathSciNetCrossRefGoogle Scholar
  2. 139.
    W.L. Hsu and G.L. Nemhauser. Easy and hard bottleneck location problems. Discrete Applied Mathematics, 1: 209–216, 1979.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vijay V. Vazirani
    • 1
  1. 1.Georgia Institute of TechnologyCollege of ComputingAtlantaUSA

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