Abstract
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(nlog2 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.
Supported in part by the Swiss National Science Foundation project 20GG21-134355, under the auspices of the ESF EUROCORES program EuroGIGA/VORONOI.
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Cheilaris, P., Khramtcova, E., Langerman, S., Papadopoulou, E. (2014). A Randomized Incremental Approach for the Hausdorff Voronoi Diagram of Non-crossing Clusters. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_9
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