{"publication_identifier":{"issn":["0179-5376"]},"date_updated":"2022-03-28T14:50:42Z","volume":10,"extern":"1","type":"journal_article","publication":"Discrete & Computational Geometry","publication_status":"published","abstract":[{"lang":"eng","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."}],"_id":"4045","doi":"10.1007/BF02573973","author":[{"last_name":"Chazelle","first_name":"Bernard","full_name":"Chazelle, Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"citation":{"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>.","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>","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 10 (1993) 183–196.","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."},"month":"12","date_created":"2018-12-11T12:06:37Z","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.","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","page":"183 - 196","intvolume":"        10","language":[{"iso":"eng"}],"publist_id":"2083","issue":"1","oa_version":"None","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02573973"}],"scopus_import":"1","quality_controlled":"1","title":"Diameter, width, closest line pair, and parametric searching","date_published":"1993-12-01T00:00:00Z","article_type":"original","publisher":"Springer","year":"1993","day":"01"}