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Assigning Weights to Minimize the Covering Radius in the Plane

Authors Eunjin Oh, Hee-Kap Ahn



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Eunjin Oh
Hee-Kap Ahn

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Eunjin Oh and Hee-Kap Ahn. Assigning Weights to Minimize the Covering Radius in the Plane. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 58:1-58:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ISAAC.2016.58

Abstract

Given a set P of n points in the plane and a multiset W of k weights with k leq n, we assign a weight in W to a point in P to minimize the maximum weighted distance from the weighted center of P to any point in P. In this paper, we give two algorithms which take O(k^2 n^2 log^4 n) time and O(k^5 n log^4 k + kn log^3 n) time, respectively. For a constant k, the second algorithm takes only O(n log^3 n) time, which is near-linear.
Keywords
  • Weighted center
  • facility location
  • weight assignment
  • combinatorial op- timization
  • computational geometry

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