[{"author":[{"first_name":"Christian","last_name":"Sohler","full_name":"Sohler, Christian"}],"title":"Generating Random Star-Shaped Polygons","date_updated":"2020-08-28T14:21:07Z","department":[{"_id":"63"}],"language":[{"iso":"eng"}],"type":"conference","status":"public","publication":"Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG'99)","user_id":"15415","citation":{"apa":"Sohler, C. (1999). Generating Random Star-Shaped Polygons. In *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)* (pp. 174–177).","ieee":"C. Sohler, “Generating Random Star-Shaped Polygons,” in *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*, 1999, pp. 174–177.","bibtex":"@inproceedings{Sohler_1999, title={Generating Random Star-Shaped Polygons}, booktitle={Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)}, author={Sohler, Christian}, year={1999}, pages={174–177} }","chicago":"Sohler, Christian. “Generating Random Star-Shaped Polygons.” In *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*, 174–77, 1999.","short":"C. Sohler, in: Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99), 1999, pp. 174–177.","mla":"Sohler, Christian. “Generating Random Star-Shaped Polygons.” *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*, 1999, pp. 174–77.","ama":"Sohler C. Generating Random Star-Shaped Polygons. In: *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*. ; 1999:174-177."},"_id":"18576","date_created":"2020-08-28T14:20:42Z","abstract":[{"lang":"eng","text":"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.

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."}],"year":"1999","page":"174-177"}]