{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T07:33:49Z","timestamp":1790235229413,"version":"4.1.0"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1998,6]]},"abstract":"<jats:p> Consider a set of n points in d-dimensional Euclidean space, d \u2265 2, each of which is continuously moving along a given individual trajectory. As the points move, their Voronoi diagram changes continuously, but at certain critical instants in time, topological events occur that cause a change in the Voronoi diagram. In this paper, we present a method of maintaining the Voronoi diagram over time, at a cost of O( log n) per event, while showing that the number of topological events has an upper bound of O(n<jats:sup>d<\/jats:sup>\u03bb<jats:sub>s<\/jats:sub>(n)), where \u03bb<jats:sub>s<\/jats:sub>(n) is the (nearly linear) maximum length of a (n,s)-Davenport-Schinzel sequence, and s is a constant depending on the motions of the point sites. <\/jats:p><jats:p> In addition, we show that if only k points are moving (while leaving the other n - k points fixed), there is an upper bound of O(kn<jats:sup>d-1<\/jats:sup>\u03bb<jats:sub>s<\/jats:sub>(n)+(n-k)<jats:sup>d<\/jats:sup>\u03bb <jats:sub>s<\/jats:sub>(k)) on the number of topological events. <\/jats:p>","DOI":"10.1142\/s0218195998000187","type":"journal-article","created":{"date-parts":[[2003,7,22]],"date-time":"2003-07-22T11:10:21Z","timestamp":1058872221000},"page":"365-379","source":"Crossref","is-referenced-by-count":54,"title":["Voronoi Diagrams of Moving Points"],"prefix":"10.1142","volume":"08","author":[{"given":"Gerhard","family":"Albers","sequence":"first","affiliation":[{"name":"Computer Science Department, University of W\u00fcrzburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leonidas J.","family":"Guibas","sequence":"additional","affiliation":[{"name":"Computer Science Department, Stanford University, Stanford, CA 94305, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph S. 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