[{"oa_version":"None","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4113","intvolume":" 38","status":"public","title":"On the number of line separations of a finite set in the plane","issue":"1","abstract":[{"text":"Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of fk(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on fk(n) is established. Both are nontrivial and improve bounds known before. In particular, is shown by exhibiting special point-sets which realize that many k-sets. In addition, is proved by the study of a combinatorial problem which is of interest in its own right.","lang":"eng"}],"type":"journal_article","date_published":"1985-01-01T00:00:00Z","citation":{"ama":"Edelsbrunner H, Welzl E. On the number of line separations of a finite set in the plane. Journal of Combinatorial Theory Series A. 1985;38(1):15-29. doi:10.1016/0097-3165(85)90017-2","ista":"Edelsbrunner H, Welzl E. 1985. On the number of line separations of a finite set in the plane. Journal of Combinatorial Theory Series A. 38(1), 15–29.","apa":"Edelsbrunner, H., & Welzl, E. (1985). On the number of line separations of a finite set in the plane. Journal of Combinatorial Theory Series A. Elsevier. https://doi.org/10.1016/0097-3165(85)90017-2","ieee":"H. Edelsbrunner and E. Welzl, “On the number of line separations of a finite set in the plane,” Journal of Combinatorial Theory Series A, vol. 38, no. 1. Elsevier, pp. 15–29, 1985.","mla":"Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations of a Finite Set in the Plane.” Journal of Combinatorial Theory Series A, vol. 38, no. 1, Elsevier, 1985, pp. 15–29, doi:10.1016/0097-3165(85)90017-2.","short":"H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 38 (1985) 15–29.","chicago":"Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations of a Finite Set in the Plane.” Journal of Combinatorial Theory Series A. Elsevier, 1985. https://doi.org/10.1016/0097-3165(85)90017-2."},"publication":"Journal of Combinatorial Theory Series A","page":"15 - 29","article_type":"original","article_processing_charge":"No","day":"01","scopus_import":"1","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Welzl, Emo","first_name":"Emo","last_name":"Welzl"}],"volume":38,"date_updated":"2022-01-31T14:14:25Z","date_created":"2018-12-11T12:07:01Z","year":"1985","publisher":"Elsevier","publication_status":"published","publist_id":"2011","extern":"1","doi":"10.1016/0097-3165(85)90017-2","language":[{"iso":"eng"}],"quality_controlled":"1","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"month":"01"}]