Computing the Map of Geometric Minimal Cuts
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Higher order Voronoi diagrams of segments for VLSI critical area extraction
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Algorithms and theory of computation handbook
Farthest-polygon Voronoi diagrams
Computational Geometry: Theory and Applications
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We study the Hausdorff Voronoi diagram of point clusters in the plane, a generalization ofVoronoi 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 Θ(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 segments between pairs of crossing clusters. 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.