[{"date_updated":"2020-08-28T14:21:07Z","language":[{}],"department":[{"tree":[{"_id":"7"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"63"}],"author":[{"last_name":"Sohler","first_name":"Christian"}],"dc":{"creator":["Sohler, Christian"],"date":["1999"],"type":["info:eu-repo/semantics/conferenceObject","doc-type:conferenceObject","text"],"identifier":["https://ris.uni-paderborn.de/record/18576"],"source":["Sohler C. Generating Random Star-Shaped Polygons. In: *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*. ; 1999:174-177."],"language":["eng"],"description":["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."],"title":["Generating Random Star-Shaped Polygons"],"rights":["info:eu-repo/semantics/closedAccess"]},"creator":{"id":"15415","login":"koala"},"dini_type":"doc-type:conferenceObject","_version":2,"page":"174-177","_id":"18576","date_created":"2020-08-28T14:20:42Z","abstract":[{"lang":"eng"}],"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.","mla":"Sohler, Christian. “Generating Random Star-Shaped Polygons.” *Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99)*, 1999, pp. 174–77.","short":"C. Sohler, in: Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG’99), 1999, pp. 174–177."},"message":" #HNIID-1530","uri_base":"https://ris.uni-paderborn.de","publication":"Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG'99)","status":"public","type":"conference"}]