--- _id: '4065' 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. 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 article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Arch full_name: Robison, Arch last_name: Robison - first_name: Xiao full_name: Shen, Xiao last_name: Shen citation: ama: Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 1990;81(2):153-164. doi:10.1016/0012-365X(90)90147-A apa: Edelsbrunner, H., Robison, A., & Shen, X. (1990). Covering convex sets with non-overlapping polygons. Discrete Mathematics. Elsevier. https://doi.org/10.1016/0012-365X(90)90147-A chicago: Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” Discrete Mathematics. Elsevier, 1990. https://doi.org/10.1016/0012-365X(90)90147-A. ieee: H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” Discrete Mathematics, vol. 81, no. 2. Elsevier, pp. 153–164, 1990. 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.” Discrete Mathematics, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:10.1016/0012-365X(90)90147-A. short: H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164. date_created: 2018-12-11T12:06:44Z date_published: 1990-04-15T00:00:00Z date_updated: 2022-02-22T15:45:55Z day: '15' doi: 10.1016/0012-365X(90)90147-A extern: '1' intvolume: ' 81' issue: '2' language: - iso: eng main_file_link: - url: https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub month: '04' oa_version: None page: 153 - 164 publication: Discrete Mathematics publication_identifier: eissn: - 1872-681X issn: - 0012-365X publication_status: published publisher: Elsevier publist_id: '2060' quality_controlled: '1' scopus_import: '1' status: public title: Covering convex sets with non-overlapping polygons type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 81 year: '1990' ...