{"volume":38,"date_updated":"2022-01-31T14:14:25Z","type":"journal_article","extern":"1","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"doi":"10.1016/0097-3165(85)90017-2","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"_id":"4113","publication":"Journal of Combinatorial Theory Series A","publication_status":"published","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"}],"article_processing_charge":"No","citation":{"apa":"Edelsbrunner, H., &#38; Welzl, E. (1985). On the number of line separations of a finite set in the plane. <i>Journal of Combinatorial Theory Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/0097-3165(85)90017-2\">https://doi.org/10.1016/0097-3165(85)90017-2</a>","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.","chicago":"Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations of a Finite Set in the Plane.” <i>Journal of Combinatorial Theory Series A</i>. Elsevier, 1985. <a href=\"https://doi.org/10.1016/0097-3165(85)90017-2\">https://doi.org/10.1016/0097-3165(85)90017-2</a>.","ieee":"H. Edelsbrunner and E. Welzl, “On the number of line separations of a finite set in the plane,” <i>Journal of Combinatorial Theory Series A</i>, vol. 38, no. 1. Elsevier, pp. 15–29, 1985.","short":"H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 38 (1985) 15–29.","mla":"Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations of a Finite Set in the Plane.” <i>Journal of Combinatorial Theory Series A</i>, vol. 38, no. 1, Elsevier, 1985, pp. 15–29, doi:<a href=\"https://doi.org/10.1016/0097-3165(85)90017-2\">10.1016/0097-3165(85)90017-2</a>.","ama":"Edelsbrunner H, Welzl E. On the number of line separations of a finite set in the plane. <i>Journal of Combinatorial Theory Series A</i>. 1985;38(1):15-29. doi:<a href=\"https://doi.org/10.1016/0097-3165(85)90017-2\">10.1016/0097-3165(85)90017-2</a>"},"date_created":"2018-12-11T12:07:01Z","month":"01","page":"15 - 29","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2011","intvolume":"        38","language":[{"iso":"eng"}],"title":"On the number of line separations of a finite set in the plane","scopus_import":"1","quality_controlled":"1","issue":"1","oa_version":"None","year":"1985","article_type":"original","publisher":"Elsevier","day":"01","date_published":"1985-01-01T00:00:00Z"}