[{"month":"04","quality_controlled":"1","publist_id":"2060","publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"article_type":"original","volume":81,"date_created":"2018-12-11T12:06:44Z","acknowledgement":"The first author acknowledges the support by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862. Work on this paper by the second author was supported by a Shell Fellowship in Computer Science. The third author as supported by the office of Naval Research under grant NOOO14-86K-0416. ","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","intvolume":"        81","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"first_name":"Arch","full_name":"Robison, Arch","last_name":"Robison"},{"last_name":"Shen","full_name":"Shen, Xiao","first_name":"Xiao"}],"_id":"4065","date_published":"1990-04-15T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1016/0012-365X(90)90147-A","publisher":"Elsevier","year":"1990","type":"journal_article","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}],"publication":"Discrete Mathematics","title":"Covering convex sets with non-overlapping polygons","citation":{"chicago":"Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>.","ieee":"H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” <i>Discrete Mathematics</i>, vol. 81, no. 2. Elsevier, pp. 153–164, 1990.","short":"H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.","mla":"Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>.","apa":"Edelsbrunner, H., Robison, A., &#38; Shen, X. (1990). Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 153–164.","ama":"Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. 1990;81(2):153-164. doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>"},"issue":"2","scopus_import":"1","publication_status":"published","page":"153 - 164","oa_version":"None","day":"15","abstract":[{"text":"We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.","lang":"eng"}],"date_updated":"2022-02-22T15:45:55Z","status":"public"},{"date_published":"1986-06-01T00:00:00Z","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"David","full_name":"Haussler, David","last_name":"Haussler"}],"_id":"4107","type":"journal_article","doi":"10.1016/0012-365X(86)90008-7","language":[{"iso":"eng"}],"year":"1986","publisher":"Elsevier","article_type":"original","volume":60,"month":"06","publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"publist_id":"2019","quality_controlled":"1","article_processing_charge":"No","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","intvolume":"        60","date_created":"2018-12-11T12:06:59Z","acknowledgement":"Research reported in the paper was conducted while the second author was visiting the Technical University of Graz. Support provided by the Technical University for this visit is gratefully acknowledged. ","day":"01","oa_version":"None","page":"139 - 146","publication_status":"published","abstract":[{"text":"A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality.","lang":"eng"}],"status":"public","date_updated":"2022-02-01T12:44:50Z","publication":"Discrete Mathematics","title":"The complexity of cells in 3-dimensional arrangements","issue":"C","citation":{"ieee":"H. Edelsbrunner and D. Haussler, “The complexity of cells in 3-dimensional arrangements,” <i>Discrete Mathematics</i>, vol. 60, no. C. Elsevier, pp. 139–146, 1986.","chicago":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>.","ama":"Edelsbrunner H, Haussler D. The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. 1986;60(C):139-146. doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>","apa":"Edelsbrunner, H., &#38; Haussler, D. (1986). The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>","mla":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>, vol. 60, no. C, Elsevier, 1986, pp. 139–46, doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>.","short":"H. Edelsbrunner, D. Haussler, Discrete Mathematics 60 (1986) 139–146.","ista":"Edelsbrunner H, Haussler D. 1986. The complexity of cells in 3-dimensional arrangements. Discrete Mathematics. 60(C), 139–146."}}]