{"abstract":[{"text":"This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n12−112+O(1)n47  points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.","lang":"eng"}],"publist_id":"2043","citation":{"apa":"Edelsbrunner, H., Hasan, N., Seidel, R., &#38; Shen, X. (1989). Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. Springer. <a href=\"https://doi.org/10.1007/BF00181432\">https://doi.org/10.1007/BF00181432</a>","chicago":"Edelsbrunner, Herbert, Nany Hasan, Raimund Seidel, and Xiao Shen. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF00181432\">https://doi.org/10.1007/BF00181432</a>.","ista":"Edelsbrunner H, Hasan N, Seidel R, Shen X. 1989. Circles through two points that always enclose many points. Geometriae Dedicata. 32(1), 1–12.","ieee":"H. Edelsbrunner, N. Hasan, R. Seidel, and X. Shen, “Circles through two points that always enclose many points,” <i>Geometriae Dedicata</i>, vol. 32, no. 1. Springer, pp. 1–12, 1989.","ama":"Edelsbrunner H, Hasan N, Seidel R, Shen X. Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. 1989;32(1):1-12. doi:<a href=\"https://doi.org/10.1007/BF00181432\">10.1007/BF00181432</a>","short":"H. Edelsbrunner, N. Hasan, R. Seidel, X. Shen, Geometriae Dedicata 32 (1989) 1–12.","mla":"Edelsbrunner, Herbert, et al. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>, vol. 32, no. 1, Springer, 1989, pp. 1–12, doi:<a href=\"https://doi.org/10.1007/BF00181432\">10.1007/BF00181432</a>."},"type":"journal_article","language":[{"iso":"eng"}],"volume":32,"year":"1989","oa_version":"None","date_published":"1989-10-01T00:00:00Z","publisher":"Springer","publication":"Geometriae Dedicata","date_updated":"2022-02-14T09:55:28Z","article_type":"original","day":"01","status":"public","scopus_import":"1","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Hasan","full_name":"Hasan, Nany","first_name":"Nany"},{"first_name":"Raimund","full_name":"Seidel, Raimund","last_name":"Seidel"},{"first_name":"Xiao","full_name":"Shen, Xiao","last_name":"Shen"}],"publication_identifier":{"issn":["0046-5755"],"eissn":["1572-9168"]},"_id":"4080","quality_controlled":"1","acknowledgement":"Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.","extern":"1","intvolume":"        32","title":"Circles through two points that always enclose many points","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","month":"10","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF00181432"}],"publication_status":"published","article_processing_charge":"No","page":"1 - 12","doi":"10.1007/BF00181432","date_created":"2018-12-11T12:06:49Z","issue":"1"}