{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:35:00Z","timestamp":1787340900285,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:p>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 $O(n\\alpha (n)\\log n)$. The analysis of the algorithm uses a novel approach that generalizes and extends the Clarkson\u2013Shor analysis technique [in Discrete Comput. Geom., 4 (1989), pp. 387\u2013421]. 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.<\/jats:p>","DOI":"10.1137\/0222077","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:38:56Z","timestamp":1109227136000},"page":"1286-1302","source":"Crossref","is-referenced-by-count":28,"title":["Computing a Face in an Arrangement of Line Segments and Related Problems"],"prefix":"10.1137","volume":"22","author":[{"given":"Bernard","family":"Chazelle","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Herbert","family":"Edelsbrunner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leonidas","family":"Guibas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Micha","family":"Sharir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jack","family":"Snoeyink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840405"},{"key":"R2","first-page":"7","volume-title":"Proc. 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Mitchell,  On Computing a Single Face in an Arrangement of Line Segments,  1990, Manuscript, School of Operations Research and Industrial Engineering, Corneal University, Ithaca, NY, July"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80064-8"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187902"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574699"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58043-7_3"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(91)90012-4"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187894"},{"key":"R20","unstructured":"E. Yaniv, Masters Thesis,  Randomized Incremental Construction of Delaunay Triangulations: Theory and Practice, M.Sc. thesis, Tel Aviv University, Tel Aviv, Israel,  1991"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0222077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:55:21Z","timestamp":1787338521000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0222077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1993,12]]}},"alternative-id":["10.1137\/0222077"],"URL":"https:\/\/doi.org\/10.1137\/0222077","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}