{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T23:44:45Z","timestamp":1648943085704},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02n03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p>This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm<jats:sup>2<\/jats:sup>+ m<jats:sup>3<\/jats:sup>+ nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m<jats:sup>2<\/jats:sup>+ n log n) time with O(m(n + m)) space and the other O(nm log n + m<jats:sup>2<\/jats:sup>log m) time with O(n + m) space.<\/jats:p>","DOI":"10.1142\/s0218195906001963","type":"journal-article","created":{"date-parts":[[2006,4,27]],"date-time":"2006-04-27T12:53:13Z","timestamp":1146142393000},"page":"117-144","source":"Crossref","is-referenced-by-count":11,"title":["VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE EUCLIDEAN PLANE"],"prefix":"10.1142","volume":"16","author":[{"given":"SANG WON","family":"BAE","sequence":"first","affiliation":[{"name":"Division of Computer Science, Korea Advanced Institute of Science and Technology, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea"}]},{"given":"KYUNG-YONG","family":"CHWA","sequence":"additional","affiliation":[{"name":"Division of Computer Science, Korea Advanced Institute of Science and Technology, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(02)00505-7"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-003-2947-0"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1145\/102782.102784"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-52055-4"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(02)00167-0"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574686"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(93)90033-3"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02523236"},{"key":"rf15","volume-title":"Introduction to Algorithms","author":"Cormen T. H.","year":"2001"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054190000072"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1109\/5.163409"},{"key":"rf18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-04245-8","volume-title":"Computational Geometry Algorithms and Applications","author":"de Berg M.","year":"2000"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195906001963","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T06:07:43Z","timestamp":1586844463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195906001963"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":12,"journal-issue":{"issue":"02n03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1142\/S0218195906001963"],"URL":"https:\/\/doi.org\/10.1142\/s0218195906001963","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}