Generating random star-shaped polygons
نویسنده
چکیده
In this paper we deal with two problems on star-shaped polygons. At rst, we present a Las-Vegas algorithm that uniformly at random creates a star-shaped polygon whose vertices are given by a point set S of n points in the plane that does not admit degenerated star-shaped polygons. The expected running time of the algorithm is O(n logn) and it uses O(n) memory. We call a starshaped polygon degenerated if its kernel has 0 area. Secondly, we show how to count all star-shaped polygons whose vertices are a subset of S in O(n logn) time and O(n) space. The algorithm can also be used for random uniform generation. We also present lower and upper bounds on the number of star-shaped polygons.
منابع مشابه
Generating Random Star-shaped Polygons (extended Abstract)
In this paper we deal with two problems on star-shaped polygons. First, we present a Las-Vegas algorithm that uniformly at random creates a star-shaped polygon whose vertices are given by a point set S of n points in the plane that does not admit degenerate star-shaped polygons. The expected running time of the algorithm is O(n 2 logn) and it uses O(n) memory. We call a star-shaped polygon dege...
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