{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:31:57Z","timestamp":1750307517992,"version":"3.41.0"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2009,10,1]],"date-time":"2009-10-01T00:00:00Z","timestamp":1254355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2009,10]]},"abstract":"<jats:p>\n            Finding the convex hull of\n            <jats:italic>n<\/jats:italic>\n            points in the plane requires\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            ) time in general. In Devroye and Toussaint [1993] and Golin et al. [2002] the problem of computing the convex hull of the intersection points of\n            <jats:italic>n<\/jats:italic>\n            lines was considered, where the lines are chosen randomly according to two various models. In both models, linear-time algorithms were developed. Here we improve the results of Devroye and Toussaint [1993] by giving a universal algorithm for a wider range of distributions.\n          <\/jats:p>","DOI":"10.1145\/1597036.1597046","type":"journal-article","created":{"date-parts":[[2009,11,4]],"date-time":"2009-11-04T18:28:31Z","timestamp":1257359311000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A linear algorithm for computing convex hulls for random lines"],"prefix":"10.1145","volume":"5","author":[{"given":"Daniel","family":"Berend","sequence":"first","affiliation":[{"name":"Ben-Gurion University, Beer-Sheva, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Braverman","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2009,11,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90010-6"},{"key":"e_1_2_1_2_1","first-page":"11","article-title":"Convex hull for intersections of random lines","volume":"25","author":"Berend D.","year":"2005","journal-title":"Proceedings of the International Conference on the Analysis of Algorithms"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02712873"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(85)90050-0"},{"key":"e_1_2_1_5_1","unstructured":"Cormen T. Leiserson G. and Rivest R. 2000. Introduction to Algorithms. The MIT Press.   Cormen T. Leiserson G. and Rivest R. 2000. Introduction to Algorithms. The MIT Press."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1993.1020"},{"volume-title":"Proceedings of the Japan Conference on Discrete and Computational Geometry (JCDCG'02)","author":"Golin M.","key":"e_1_2_1_7_1"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(72)90045-2"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(73)90020-3"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/0215021"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(87)90086-X"},{"volume-title":"Computational Geometry: An Introduction","year":"1986","author":"Preparata F.","key":"e_1_2_1_12_1"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1597036.1597046","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1597036.1597046","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:18:11Z","timestamp":1750249091000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1597036.1597046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["10.1145\/1597036.1597046"],"URL":"https:\/\/doi.org\/10.1145\/1597036.1597046","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2009,10]]},"assertion":[{"value":"2005-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-11-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}