[{"publication_status":"published","publication_identifier":{"issn":["0209-9683"]},"language":[{"iso":"eng"}],"issue":"3","volume":12,"abstract":[{"text":"We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m2/3n2/3+nα(n)+nlog m). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is Ω(m2/3n2/3+nα(n)). In addition, we show that the number of edges bounding any m faces in an arrangement of n line segments with a total of t intersecting pairs is O(m2/3t1/3+nα(t/n)+nmin{log m,log t/n}), almost matching the lower bound of Ω(m2/3t1/3+nα(t/n)) demonstrated in this paper.","lang":"eng"}],"oa_version":"None","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01285815"}],"scopus_import":"1","intvolume":" 12","month":"09","date_updated":"2022-03-15T15:44:26Z","extern":"1","_id":"4053","article_type":"original","type":"journal_article","status":"public","year":"1992","publication":"Combinatorica","day":"01","page":"261 - 274","date_created":"2018-12-11T12:06:40Z","doi":"10.1007/BF01285815","date_published":"1992-09-01T00:00:00Z","quality_controlled":"1","publisher":"Springer","citation":{"mla":"Aronov, Boris, et al. “The Number of Edges of Many Faces in a Line Segment Arrangement.” Combinatorica, vol. 12, no. 3, Springer, 1992, pp. 261–74, doi:10.1007/BF01285815.","ieee":"B. Aronov, H. Edelsbrunner, L. Guibas, and M. Sharir, “The number of edges of many faces in a line segment arrangement,” Combinatorica, vol. 12, no. 3. Springer, pp. 261–274, 1992.","short":"B. Aronov, H. Edelsbrunner, L. Guibas, M. Sharir, Combinatorica 12 (1992) 261–274.","apa":"Aronov, B., Edelsbrunner, H., Guibas, L., & Sharir, M. (1992). The number of edges of many faces in a line segment arrangement. Combinatorica. Springer. https://doi.org/10.1007/BF01285815","ama":"Aronov B, Edelsbrunner H, Guibas L, Sharir M. The number of edges of many faces in a line segment arrangement. Combinatorica. 1992;12(3):261-274. doi:10.1007/BF01285815","chicago":"Aronov, Boris, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. “The Number of Edges of Many Faces in a Line Segment Arrangement.” Combinatorica. Springer, 1992. https://doi.org/10.1007/BF01285815.","ista":"Aronov B, Edelsbrunner H, Guibas L, Sharir M. 1992. The number of edges of many faces in a line segment arrangement. Combinatorica. 12(3), 261–274."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","author":[{"first_name":"Boris","last_name":"Aronov","full_name":"Aronov, Boris"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"publist_id":"2074","title":"The number of edges of many faces in a line segment arrangement"}]