On topological changes in the Delaunay triangulation of moving points

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Abstract

Let P be a collection of n points moving along pseudo-algebraic trajectories in the plane. 1 One of the hardest open problems in combinatorial and computational geometry is to obtain a nearly quadratic upper bound, or at least a subcubic bound, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during the motion of the points of P. In this paper we obtain an upper bound of O(n 2+ε), for any ε > 0, under the assumptions that (i) any four points can be co-circular at most twice, and (ii) either no ordered triple of points can be collinear more than once, or no triple of points can be collinear more than twice.

Original languageEnglish
Title of host publicationProceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012
Pages1-10
Number of pages10
DOIs
StatePublished - 23 Jul 2012
Externally publishedYes
Event28th Annual Symposuim on Computational Geometry, SCG 2012 - Chapel Hill, NC, United States
Duration: 17 Jun 201220 Jun 2012

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference28th Annual Symposuim on Computational Geometry, SCG 2012
Country/TerritoryUnited States
CityChapel Hill, NC
Period17/06/1220/06/12

Keywords

  • Delaunay triangulation
  • Discrete changes
  • Kinetic algorithms
  • Moving points
  • Voronoi diagram

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