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Separating translates in the plane: Combinatorial bounds and an algorithm

  • Jurek Czyzowicz
  • Hazel Everett
  • Jean-Marc Robert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 824)

Abstract

In this paper, we establish two combinatorial bounds related to the separation problem for sets of n pairwise disjoint translates of convex objects: 1) there exists a line which separates one translate from at least n — co√n translates, for some constant c that depends on the “shape” of the translates and 2) there is a function f such that there exists a line with orientation Θ or f(Θ) which separates one translate from at least ⌈3n⌉/4-4 translates, for any orientation Θ (f is defined only by the “shape” of the translate). We also present an O(n log (n+k)+k) time algorithm for finding a translate which can be separated from the maximum number of translates amongst sets of n pairwise disjoint translates of convex k-gons.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Hazel Everett
    • 2
  • Jean-Marc Robert
    • 3
  1. 1.Dép. d'informatiqueUniversité du Québec à HullSucc. BCanada
  2. 2.Dép. de mathématiques et d'informatiqueUniversité du Québec à MontréalSucc. Centre-VilleCanada
  3. 3.Dép. d'informatique et de mathématiqueUniversité du Québec à ChicoutimiChicoutimiCanada

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