{"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02573973"}],"publication_identifier":{"issn":["0179-5376"]},"_id":"4045","doi":"10.1007/BF02573973","publication":"Discrete & Computational Geometry","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","title":"Diameter, width, closest line pair, and parametric searching","issue":"1","article_type":"original","status":"public","article_processing_charge":"No","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Guibas","full_name":"Guibas, Leonidas","first_name":"Leonidas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"year":"1993","citation":{"mla":"Chazelle, Bernard, et al. “Diameter, Width, Closest Line Pair, and Parametric Searching.” <i>Discrete &#38; Computational Geometry</i>, vol. 10, no. 1, Springer, 1993, pp. 183–96, doi:<a href=\"https://doi.org/10.1007/BF02573973\">10.1007/BF02573973</a>.","ama":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M. Diameter, width, closest line pair, and parametric searching. <i>Discrete &#38; Computational Geometry</i>. 1993;10(1):183-196. doi:<a href=\"https://doi.org/10.1007/BF02573973\">10.1007/BF02573973</a>","ieee":"B. Chazelle, H. Edelsbrunner, L. Guibas, and M. Sharir, “Diameter, width, closest line pair, and parametric searching,” <i>Discrete &#38; Computational Geometry</i>, vol. 10, no. 1. Springer, pp. 183–196, 1993.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 10 (1993) 183–196.","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1993). Diameter, width, closest line pair, and parametric searching. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02573973\">https://doi.org/10.1007/BF02573973</a>","ista":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M. 1993. Diameter, width, closest line pair, and parametric searching. Discrete &#38; Computational Geometry. 10(1), 183–196.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. “Diameter, Width, Closest Line Pair, and Parametric Searching.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1993. <a href=\"https://doi.org/10.1007/BF02573973\">https://doi.org/10.1007/BF02573973</a>."},"type":"journal_article","date_created":"2018-12-11T12:06:37Z","publist_id":"2083","extern":"1","intvolume":"        10","acknowledgement":"*Work by Bernard Chazelle was supported by NSF Grant CCR-90-02352. Work by Herbert Edelsbrunner was supported by NSF Grant CCR-89-21421. Work by Leonidas Guibas and Micha Sharir was supported by a grant from the U.S.-Israeli Binational Science Foundation. Work by Micha Sharir was also supported by ONR Grant N00014-90-J-1284, by NSF Grant CCR-89-01484, and by grants from the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.","scopus_import":"1","date_updated":"2022-03-28T14:50:42Z","publisher":"Springer","oa_version":"None","volume":10,"day":"01","publication_status":"published","month":"12","abstract":[{"text":"We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improved solutions for them. We obtain, for any fixed ε&gt;0, an O(n1+ε) algorithm for computing the diameter of a point set in 3-space, an O(8/5+ε) algorithm for computing the width of such a set, and on O(n8/5+ε) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic.","lang":"eng"}],"date_published":"1993-12-01T00:00:00Z","page":"183 - 196"}