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A randomized incremental approach for the hausdorff voronoi diagram of non-crossing clusters

par Cheilaris, Panagiotis;Khramtcova, Elena ;Papadopoulou, Evanthia;Langerman, Stefan
Référence Lecture notes in computer science, 8392 LNCS, page (96-107)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

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(n log2 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. © 2014 Springer-Verlag Berlin Heidelberg.