{"day":"15","page":"153 - 164","issue":"2","intvolume":"        81","date_created":"2018-12-11T12:06:44Z","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0012-365X"],"eissn":["1872-681X"]},"article_processing_charge":"No","title":"Covering convex sets with non-overlapping polygons","oa_version":"None","date_published":"1990-04-15T00:00:00Z","abstract":[{"lang":"eng","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."}],"type":"journal_article","publist_id":"2060","article_type":"original","publisher":"Elsevier","year":"1990","_id":"4065","doi":"10.1016/0012-365X(90)90147-A","quality_controlled":"1","date_updated":"2022-02-22T15:45:55Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Robison, Arch","first_name":"Arch","last_name":"Robison"},{"full_name":"Shen, Xiao","first_name":"Xiao","last_name":"Shen"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","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. ","status":"public","publication_status":"published","publication":"Discrete Mathematics","month":"04","citation":{"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>","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>","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.","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 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>."},"volume":81,"extern":"1","scopus_import":"1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}]}