{"title":"Optimal time bounds for some proximity problems in the plane","date_updated":"2022-03-16T09:20:13Z","page":"55 - 60","scopus_import":"1","article_type":"original","acknowledgement":"Research supported by the National Science Foundation under Grant CCR-8714565.","quality_controlled":"1","abstract":[{"text":"Given a sequence of n points that form the vertices of a simple polygon, we show that determining a closest pair requires OMEGA(n log n) time in the algebraic decision tree model. Together with the well-known O(n log n) upper bound for finding a closest pair, this settles an open problem of Lee and Preparata. We also extend this O(n log n) upper bound to the following problem: Given a collection of sets with a total of n points in the plane, find for each point a closest neighbor that does not belong to the same set.","lang":"eng"}],"publication":"Information Processing Letters","issue":"1","day":"27","language":[{"iso":"eng"}],"publisher":"Elsevier","date_published":"1992-04-27T00:00:00Z","author":[{"last_name":"Aggarwal","full_name":"Aggarwal, Alok","first_name":"Alok"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Raghavan","full_name":"Raghavan, Prabhakar","first_name":"Prabhakar"},{"first_name":"Prasoon","full_name":"Tiwari, Prasoon","last_name":"Tiwari"}],"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/002001909290133G"}],"citation":{"ista":"Aggarwal A, Edelsbrunner H, Raghavan P, Tiwari P. 1992. Optimal time bounds for some proximity problems in the plane. Information Processing Letters. 42(1), 55–60.","chicago":"Aggarwal, Alok, Herbert Edelsbrunner, Prabhakar Raghavan, and Prasoon Tiwari. “Optimal Time Bounds for Some Proximity Problems in the Plane.” <i>Information Processing Letters</i>. Elsevier, 1992. <a href=\"https://doi.org/10.1016/0020-0190(92)90133-G\">https://doi.org/10.1016/0020-0190(92)90133-G</a>.","ama":"Aggarwal A, Edelsbrunner H, Raghavan P, Tiwari P. Optimal time bounds for some proximity problems in the plane. <i>Information Processing Letters</i>. 1992;42(1):55-60. doi:<a href=\"https://doi.org/10.1016/0020-0190(92)90133-G\">10.1016/0020-0190(92)90133-G</a>","ieee":"A. Aggarwal, H. Edelsbrunner, P. Raghavan, and P. Tiwari, “Optimal time bounds for some proximity problems in the plane,” <i>Information Processing Letters</i>, vol. 42, no. 1. Elsevier, pp. 55–60, 1992.","short":"A. Aggarwal, H. Edelsbrunner, P. Raghavan, P. Tiwari, Information Processing Letters 42 (1992) 55–60.","apa":"Aggarwal, A., Edelsbrunner, H., Raghavan, P., &#38; Tiwari, P. (1992). Optimal time bounds for some proximity problems in the plane. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/0020-0190(92)90133-G\">https://doi.org/10.1016/0020-0190(92)90133-G</a>","mla":"Aggarwal, Alok, et al. “Optimal Time Bounds for Some Proximity Problems in the Plane.” <i>Information Processing Letters</i>, vol. 42, no. 1, Elsevier, 1992, pp. 55–60, doi:<a href=\"https://doi.org/10.1016/0020-0190(92)90133-G\">10.1016/0020-0190(92)90133-G</a>."},"year":"1992","volume":42,"status":"public","publication_status":"published","intvolume":"        42","date_created":"2018-12-11T12:06:38Z","article_processing_charge":"No","publist_id":"2080","extern":"1","doi":"10.1016/0020-0190(92)90133-G","month":"04","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4048","oa_version":"None","type":"journal_article","publication_identifier":{"eissn":["1872-6119"],"issn":["0020-0190"]}}