{"oa_version":"None","article_type":"original","status":"public","extern":"1","publisher":"SIAM","issue":"6","publication_identifier":{"issn":["0097-5397"]},"year":"1993","abstract":[{"lang":"eng","text":"This paper presents a randomized incremental algorithm for computing a single face in an arrangement of n line segments in the plane that is fairly simple to implement. The expected running time of the algorithm is O(nα(n)log n). The analysis of the algorithm uses a novel approach that generalizes and extends the Clarkson-Shor analysis technique [in Discrete Comput. Geom., 4(1989), pp. 387-421]. A few extensions of the technique, obtaining efficient randomized incremental algorithms for constructing the entire arrangement of a collection of line segments and for computing a single face in an arrangement of Jordan arcs are also presented."}],"acknowledgement":"The authors wish to express their gratitude for the generous support and hospitality of the DEC Palo Alto Systems Research Center.","title":"Computing a face in an arrangement of line segments and related problems","month":"12","date_updated":"2022-03-30T08:07:21Z","scopus_import":"1","article_processing_charge":"No","date_created":"2018-12-11T12:06:34Z","type":"journal_article","citation":{"chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Jack Snoeyink. “Computing a Face in an Arrangement of Line Segments and Related Problems.” <i>SIAM Journal on Computing</i>. SIAM, 1993. <a href=\"https://doi.org/10.1137/0222077 \">https://doi.org/10.1137/0222077 </a>.","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &#38; Snoeyink, J. (1993). Computing a face in an arrangement of line segments and related problems. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0222077 \">https://doi.org/10.1137/0222077 </a>","ama":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Snoeyink J. Computing a face in an arrangement of line segments and related problems. <i>SIAM Journal on Computing</i>. 1993;22(6):1286-1302. doi:<a href=\"https://doi.org/10.1137/0222077 \">10.1137/0222077 </a>","ieee":"B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and J. Snoeyink, “Computing a face in an arrangement of line segments and related problems,” <i>SIAM Journal on Computing</i>, vol. 22, no. 6. SIAM, pp. 1286–1302, 1993.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, J. Snoeyink, SIAM Journal on Computing 22 (1993) 1286–1302.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Snoeyink J. 1993. Computing a face in an arrangement of line segments and related problems. SIAM Journal on Computing. 22(6), 1286–1302.","mla":"Chazelle, Bernard, et al. “Computing a Face in an Arrangement of Line Segments and Related Problems.” <i>SIAM Journal on Computing</i>, vol. 22, no. 6, SIAM, 1993, pp. 1286–302, doi:<a href=\"https://doi.org/10.1137/0222077 \">10.1137/0222077 </a>."},"page":"1286 - 1302","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","quality_controlled":"1","publist_id":"2087","language":[{"iso":"eng"}],"intvolume":"        22","main_file_link":[{"url":"https://epubs.siam.org/doi/10.1137/0222077"}],"volume":22,"_id":"4036","doi":"10.1137/0222077 ","author":[{"full_name":"Chazelle, Bernard","last_name":"Chazelle","first_name":"Bernard"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"},{"first_name":"Jack","last_name":"Snoeyink","full_name":"Snoeyink, Jack"}],"publication":"SIAM Journal on Computing","day":"01","publication_status":"published","date_published":"1993-12-01T00:00:00Z"}