{"doi":"10.1016/0890-5401(88)90049-1","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/0890540188900491?via%3Dihub"}],"_id":"4090","type":"journal_article","publist_id":"2029","volume":77,"acknowledgement":"Research of the first author is supported by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862; research of the second author is supported by NSF Grant ECS 84-10902.","quality_controlled":"1","title":"Minimum polygonal separation","date_published":"1988-06-01T00:00:00Z","article_processing_charge":"No","extern":"1","date_updated":"2022-02-08T10:36:30Z","status":"public","page":"218 - 232","publication_status":"published","scopus_import":"1","intvolume":"        77","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","abstract":[{"text":"In this paper we study the problem of polygonal separation in the plane, i.e., finding a convex polygon with minimum number k of sides separating two given finite point sets (k-separator), if it exists. We show that for k = Θ(n),  is a lower bound to the running time of any algorithm for this problem, and exhibit two algorithms of distinctly different flavors. The first relies on an O(n log n)-time preprocessing task, which constructs the convex hull of the internal set and a nested star-shaped polygon determined by the external set; the k-separator is contained in the annulus between the boundaries of these two polygons and is constructed in additional linear time. The second algorithm adapts the prune-and-search approach, and constructs, in each iteration, one side of the separator; its running time is O(kn), but the separator may have one more side than the minimum.","lang":"eng"}],"oa_version":"None","publication":"Information and Computation","citation":{"ieee":"H. Edelsbrunner and F. Preparata, “Minimum polygonal separation,” <i>Information and Computation</i>, vol. 77, no. 3. Elsevier, pp. 218–232, 1988.","mla":"Edelsbrunner, Herbert, and Franco Preparata. “Minimum Polygonal Separation.” <i>Information and Computation</i>, vol. 77, no. 3, Elsevier, 1988, pp. 218–32, doi:<a href=\"https://doi.org/10.1016/0890-5401(88)90049-1\">10.1016/0890-5401(88)90049-1</a>.","ama":"Edelsbrunner H, Preparata F. Minimum polygonal separation. <i>Information and Computation</i>. 1988;77(3):218-232. doi:<a href=\"https://doi.org/10.1016/0890-5401(88)90049-1\">10.1016/0890-5401(88)90049-1</a>","ista":"Edelsbrunner H, Preparata F. 1988. Minimum polygonal separation. Information and Computation. 77(3), 218–232.","short":"H. Edelsbrunner, F. Preparata, Information and Computation 77 (1988) 218–232.","chicago":"Edelsbrunner, Herbert, and Franco Preparata. “Minimum Polygonal Separation.” <i>Information and Computation</i>. Elsevier, 1988. <a href=\"https://doi.org/10.1016/0890-5401(88)90049-1\">https://doi.org/10.1016/0890-5401(88)90049-1</a>.","apa":"Edelsbrunner, H., &#38; Preparata, F. (1988). Minimum polygonal separation. <i>Information and Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/0890-5401(88)90049-1\">https://doi.org/10.1016/0890-5401(88)90049-1</a>"},"publication_identifier":{"eissn":["0890-5401"]},"month":"06","issue":"3","year":"1988","language":[{"iso":"eng"}],"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Franco","full_name":"Preparata, Franco","last_name":"Preparata"}],"article_type":"original","day":"01","publisher":"Elsevier","oa":1,"date_created":"2018-12-11T12:06:53Z"}