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 n∈ for some ∈ > 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 ∈ > 0 such that the problem cannot be approximated with an approximation ratio of 1 + ∈.
CITATION STYLE
Eidenbenz, S. (1999). How many people can hide in a terrain? In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1741, pp. 184–194). Springer Verlag. https://doi.org/10.1007/3-540-46632-0_20
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