A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of
Non-crossing Clusters
release_355vmuz7zrdepeqdu5tlrnc26e
by
Panagiotis Cheilaris, Elena Khramtcova, Stefan Langerman, Evanthia
Papadopoulou
2016
Abstract
In the Hausdorff Voronoi diagram of a family of clusters of points 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 is
defined in a nearest-neighbor sense for the input clusters. In this paper we
consider
which the combinatorial complexity of the Hausdorff Voronoi diagram is linear
in the total number of points, n, on the convex hulls of all clusters. We
present a randomized incremental construction, based on point location, that
computes this diagram in expected O(n^2n) time and expected O(n)
space. Our techniques 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. The
diagram finds direct applications in VLSI computer-aided design.
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