2014/01/07 by Sariel Har-Peled, Har-Peled, Sariel, Benjamin Raichel +1
Computer Science · Mathematics · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Computer and information sciences #Point processes and geometric inequalities #cs.CG
paper · pdf · doi:10.48550/arxiv.1401.1477
openalex publication_date 2014/01/07 · arxiv created 2015/03/19 · arxiv updated 2015/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we provide an O(n polylog n) bound on the expected complexity of the randomly weighted Voronoi diagram of a set of n sites in the plane, where the sites can be either points, interior-disjoint convex sets, or other more general objects. Here the randomness is on the weight of the sites, not their location. This compares favorably with the worst case complexity of these diagrams, which is quadratic. As a consequence we get an alternative proof to that of Agarwal etal [AHKS13] of the near linear complexity of the union of randomly expanded disjoint segments or convex sets (with an improved bound on the latter). The technique we develop is elegant and should be applicable to other problems.