A Randomized Incremental Approach for the Hausdorff Voronoi Diagram of Non-crossing Clusters

  • Panagiotis Cheilaris
  • Elena Khramtcova
  • Stefan Langerman
  • Evanthia Papadopoulou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram reveals the nearest cluster to t. This diagram finds direct applications in VLSI computer-aided design. In this paper, we consider “non-crossing” clusters, for which the combinatorial complexity of the diagram is linear in the total number n of points on the convex hulls of all clusters. We present a randomized incremental construction, based on point-location, to compute the diagram in expected O(nlog2 n) time and expected O(n) space, which considerably improves previous results. Our technique efficiently handles non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions.


Point Location Voronoi Diagram Query Point Voronoi Region Incremental Construction 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Panagiotis Cheilaris
    • 1
  • Elena Khramtcova
    • 1
  • Stefan Langerman
    • 2
  • Evanthia Papadopoulou
    • 1
  1. 1.Faculty of InformaticsUniversità della Svizzera italianaLuganoSwitzerland
  2. 2.Départment d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium

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