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How Many People Can Hide in a Terrain?

  • Stephan Eidenbenz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

How many people can hide in a given terrain, without any two of them seeing each other? We are interested in finding the precise number and an optimal placement of people to be hidden, given a terrain with n vertices. In this paper, we show that this is not at all easy: The problem of placing a maximum number of hiding people is almost as hard to approximate as the Maximum Clique problem, i.e., it cannot be approximated by any polynomial-time algorithm with an approximation ratio of nε for some ε > 0, unless P = NP. This is already true for a simple polygon with holes (instead of a terrain). If we do not allow holes in the polygon, we show that there is a constant ε > 0 such that the problem cannot be approximated with an approximation ratio of 1 + ε.

Keywords

Approximation Ratio Maximum Clique Truth Assignment Simple Polygon Maximum Cardinality 
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 1999

Authors and Affiliations

  • Stephan Eidenbenz
    • 1
  1. 1.Institute for Theoretical Computer ScienceETHSwitzerland

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