Rectilinear Covering for Imprecise Input Points

(Extended Abstract)
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)


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.


Side Length Voronoi Diagram Delaunay Triangulation Decision Algorithm Input Point 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  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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