Randomized incremental construction of the Hausdorff Voronoi diagram of non-crossing clusters [article]

Panagiotis Cheilaris, Elena Khramtcova, Evanthia Papadopoulou
2013 arXiv   pre-print
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design. We consider so-called "non-crossing" clusters. The complexity of the Hausdorff diagram of m such clusters is linear in the total number n of points in the convex hulls of all clusters. We present randomized incremental constructions for computing efficiently
more » ... he diagram, improving considerably previous results. Our best complexity algorithm runs in expected time O((n + m(log log(n))^2)log^2(n)) and worst-case space O(n). We also provide a more practical algorithm whose expected running time is O((n + m log(n))log^2(n)) and expected space complexity is O(n). To achieve these bounds, we augment the randomized incremental paradigm for the construction of Voronoi diagrams with the ability to efficiently handle 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.
arXiv:1306.5838v2 fatcat:hywesrznhzcgjhyrekugnpl2he