Finding the Θ-guarded region

  • Authors:
  • Domagoj Matijević;Ralf Osbild

  • Affiliations:
  • Department of Mathematics, J.J. Strossmayer University, Osijek, Croatia;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2010

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Abstract

We are given a finite set of n points (guards) G in the plane R^2 and an angle 0==@p2. In case @Q is bounded from below by a positive constant, we prove an almost linear bound O(n^1^+^@e) for any @e0 on the complexity. Moreover, we show that there is a sequence of inputs such that the asymptotic bound on the complexity of their @Q-region is @W(n^2).