{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T17:18:55Z","timestamp":1648747135964},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2006,8]]},"abstract":"<jats:p> For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment [Formula: see text] is equidistant to both p and q. We show that those bisectors have nice properties and, therefore, this new structure can be computed in O(n log n) time and O(n) space both for nearest-site and furthest-site versions. Also, we prove that the dynamic version of this diagram can be built in O(n<jats:sup>2<\/jats:sup>\u03bb<jats:sub>6s+2<\/jats:sub>(n) log n) time complexity, where s is a constant depending on the function that describes the motion of the points. Finally, we show how to use these structures for solving several locational optimization problems. <\/jats:p>","DOI":"10.1142\/s0218195906002051","type":"journal-article","created":{"date-parts":[[2006,8,7]],"date-time":"2006-08-07T06:44:32Z","timestamp":1154933072000},"page":"315-332","source":"Crossref","is-referenced-by-count":0,"title":["THE ANCHORED VORONOI DIAGRAM: STATIC, DYNAMIC VERSIONS AND APPLICATIONS"],"prefix":"10.1142","volume":"16","author":[{"given":"J. M.","family":"D\u00cdAZ-B\u00c1\u00d1EZ","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Camino de los Descubrimientos, s\/n 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"G\u00d3MEZ","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Madrid, Carretera de Valencia, Km. 7, s\/n 28031 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"VENTURA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Huelva, Bulevar de las Artes y las Ciencias s\/n Huelva, 21071 Huelva, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1145\/116873.116880"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(03)00015-4"},{"key":"rf3","first-page":"650","volume":"24","author":"Canny J. F.","journal-title":"SIAM J. Computing"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.12.4.317.11880"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24767-8_22"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2004.09.006"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(02)00647-1"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187681"},{"key":"rf9","first-page":"67","volume":"9","author":"Edelsbrunner H.","journal-title":"ACM Trans. Graph."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/9789814355858_0006"},{"key":"rf11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/3-540-55121-2_11","volume":"570","author":"Guibas L.","year":"1991"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0453-4514(99)80004-0"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-52055-4"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(93)90033-3"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195901000663"},{"key":"rf16","volume-title":"Spatial Tessellations: Concepts and Applications of Voronoi Diagrams","author":"Okabe A.","year":"1992"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(97)80001-X"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009330"},{"key":"rf19","volume-title":"Davenport-Schinzel Sequences and Their Geometric Applications","author":"Sharir M.","year":"1995"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195906002051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:30:16Z","timestamp":1565123416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195906002051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8]]},"references-count":19,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,8]]}},"alternative-id":["10.1142\/S0218195906002051"],"URL":"https:\/\/doi.org\/10.1142\/s0218195906002051","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,8]]}}}