{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:12:52Z","timestamp":1760440372281},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1992,6]]},"abstract":"<jats:p> We describe randomized parallel algorithms for building trapezoidal diagrams of line segments in the plane. The algorithms are designed for a CRCW PRAM. For general segments, we give an algorithm requiring optimal O(A+n log n) expected work and optimal O( log n) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O( log n log log n log * n) expected time , and a simpler algorithm requiring O(n log * n) expected work. The serial algorithm corresponding to the latter is among the simplest known algorithms requiring O(n log * n) expected operations. For a set of segments forming K chains, we give an algorithm requiring O(A+n log * n+K log n) expected work and O( log n log log n log * n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps. <\/jats:p>","DOI":"10.1142\/s0218195992000081","type":"journal-article","created":{"date-parts":[[2004,11,25]],"date-time":"2004-11-25T00:50:24Z","timestamp":1101343824000},"page":"117-133","source":"Crossref","is-referenced-by-count":10,"title":["RANDOMIZED PARALLEL ALGORITHMS FOR TRAPEZOIDAL DIAGRAMS"],"prefix":"10.1142","volume":"02","author":[{"given":"KENNETH L.","family":"CLARKSON","sequence":"first","affiliation":[{"name":"AT&amp;T Bell Laboratories, Room 2C-455, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RICHARD","family":"COLE","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University, New York, New York, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ROBERT E.","family":"TARJAN","sequence":"additional","affiliation":[{"name":"Princeton University and NEC Research Institute, Princeton, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195992000081","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:57:41Z","timestamp":1565135861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195992000081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,6]]},"references-count":0,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1992,6]]}},"alternative-id":["10.1142\/S0218195992000081"],"URL":"https:\/\/doi.org\/10.1142\/s0218195992000081","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,6]]}}}