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.
CITATION STYLE
Cheilaris, P., Khramtcova, E., Langerman, S., & Papadopoulou, E. (2014). A randomized incremental approach for the hausdorff voronoi diagram of non-crossing clusters. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8392 LNCS, pp. 96–107). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_9
Mendeley helps you to discover research relevant for your work.