The Hausdorff Voronoi Diagram of Point Clusters in the Plane

We study the Hausdorff Voronoi diagram of point clusters in the plane, a generalization of Voronoi diagrams based on the Hausdorff distance function. We derive a tight combinatorial bound on the structural complexity of this diagram and present a plane sweep algorithm for its construction. In particular, we show that the size of the Hausdorff Voronoi diagram is (n + m), where n is the number of points on the convex hulls of the given clusters, and m is the number of crucial supporting segments1 between pairs of crossing clusters2 . The plane sweep algorithm generalizes the standard plane sweep paradigm for the construction of Voronoi diagrams with the ability to handle disconnected Hausdorff Voronoi regions. The Hausdorff Voronoi diagram finds direct application in the problem of computing the critical area of a VLSI Layout, a measure reflecting the sensitivity of the VLSI design to spot defects during manufacturing. Key Words. Voronoi diagram, Hausdorff distance, plane sweep, VLSI yi...

• Type: Journal
• Year: 2004
• Where: ALGORITHMICA
• Authors: Evanthia Papadopoulou
• Keywords: ALGORITHMICA 2004, Hausdorff Voronoi Diagram, Plane Sweep, Plane Sweep Algorithm