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Rectilinear Covering for Imprecise Input Points

(Extended Abstract)
  • Hee-Kap Ahn
  • Sang Won Bae
  • Shin-ichi Tanigawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)

Abstract

We consider the rectilinear k-center problem in the presence of impreciseness of input points. We assume that the input is a set S of n unit squares, possibly overlapping each other, each of which is interpreted as a measured point with an identical error bound under the L  ∞  metric on ℝ2. Our goal, in this work, is to analyze the worst situation with respect to the rectilinear k-center for a given set S of unit squares. For the purpose, we are interested in a value λ k (S) that is the minimum side length of k congruent squares by which any possible true point set from S can be covered. We show that, for k = 1 or 2, computing λ k (S) is equivalent to the problem of covering the input squares S completely by k squares, and thus one can solve the problem in linear time. However, for k ≥ 3, this is not the case, and we present an O(n logn)-time algorithm for computing λ 3(S). For structural observations, we introduce a new notion on geometric covering, namely the covering-family, which is of independent interest.

Keywords

Side Length Voronoi Diagram Delaunay Triangulation Decision Algorithm Input Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Sang Won Bae
    • 2
  • Shin-ichi Tanigawa
    • 3
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangKorea
  2. 2.Department of Computer ScienceKyonggi UniversitySuwonKorea
  3. 3.Research Institute for Mathematical ScienceKyoto UniversityKyotoJapan

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