Randomized incremental construction of the Hausdorff Voronoi diagram of non-crossing clusters release_hywesrznhzcgjhyrekugnpl2he

by Panagiotis Cheilaris, Elena Khramtcova, Evanthia Papadopoulou

Released as a article .

2013  

Abstract

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 the 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.
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Type  article
Stage   submitted
Date   2013-12-16
Version   v2
Language   en ?
arXiv  1306.5838v2
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