Generating Random Star-Shaped Polygons
Sohler, Christian
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^2log n) ) and it uses ( O(n) ) memory. We call a star-shaped polygon degenerate if its kernel has 0 area.<br><br>Secondly, we show how to count all star-shaped polygons whose vertices are a subset of ( S ) in ( O(n^5log n) ) 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.
1999
info:eu-repo/semantics/conferenceObject
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text
https://ris.uni-paderborn.de/record/18576
Sohler C. Generating Random Star-Shaped Polygons. In: <i>Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCGâ€™99)</i>. ; 1999:174-177.
eng
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