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

In the Hausdorff Voronoi diagram of a family of clusters of points 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 is defined in a nearest-neighbor sense for the input clusters. In this paper we consider non-crossing clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, n , on the convex hulls of all clusters. We present a randomized incremental construction, based on point location, that computes this diagram in expected O(nlog ^2n) time and expected O ( n ) space. Our techniques efficiently handle 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. The diagram finds direct applications in VLSI computer-aided design.