{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:21:39Z","timestamp":1759638099967},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> The farthest line-segment Voronoi diagram illustrates properties surprisingly different from its counterpart for points: Voronoi regions may be disconnected and they are not characterized by convex-hull properties. In this paper we introduce the farthest hull and its Gaussian map as a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and derive tighter bounds on the (linear) size of this diagram. With the purpose of unifying construction algorithms for farthest-point and farthest line-segment Voronoi diagrams, we adapt standard techniques to construct a convex hull and compute the farthest hull in O(n log n) or output sensitive O(n log h) time, where n is the number of line-segments and h is the number of faces in the corresponding farthest Voronoi diagram. As a result, the farthest line-segment Voronoi diagram can be constructed in output sensitive O(n log h) time. Our algorithms are given in the Euclidean plane but they hold also in the general L<jats:sub>p<\/jats:sub> metric, 1 \u2264 p \u2264 \u221e. <\/jats:p>","DOI":"10.1142\/s0218195913600121","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T02:29:37Z","timestamp":1405391377000},"page":"443-459","source":"Crossref","is-referenced-by-count":12,"title":["ON THE FARTHEST LINE-SEGMENT VORONOI DIAGRAM"],"prefix":"10.1142","volume":"23","author":[{"given":"EVANTHIA","family":"PAPADOPOULOU","sequence":"first","affiliation":[{"name":"Faculty of Informatics, USI - Universit\u00e0 della Svizzera italiana, Lugano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SANDEEP KUMAR","family":"DEY","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, USI - Universit\u00e0 della Svizzera italiana, Lugano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,7,14]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187749"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2006.07.008"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02712873"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(93)90103-U"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2010.11.004"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934440"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1145\/322217.322219"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1137\/0210006"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195901000663"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2010.2100550"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195904001536"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195913600121","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:28:35Z","timestamp":1565188115000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195913600121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":11,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2014,7,14]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S0218195913600121"],"URL":"https:\/\/doi.org\/10.1142\/s0218195913600121","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}