The Hausdorff Voronoi Diagram of Point Clusters in the Plane
نویسندگان
چکیده
منابع مشابه
Randomized Incremental Construction for the Hausdorff Voronoi Diagram of point clusters
This paper applies the randomized incremental construction (RIC) framework to computing the Hausdorff Voronoi diagram of a family of k clusters of points in the plane. The total number of points is n. The diagram is a generalization of Voronoi diagrams based on the Hausdorff distance function. The combinatorial complexity of the Hausdorff Voronoi diagram is O(n + m), where m is the total number...
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We revisit the L∞ Hausdorff Voronoi diagram of clusters of points, equivalently, the L∞ Hausdorff Voronoi diagram of rectangles, and present a plane sweep algorithm for its construction that generalizes and improves upon previous results. We show that the structural complexity of the L∞ Hausdorff Voronoi diagram is Θ(n+m), where n is the number of given clusters and m is the number of essential...
متن کاملRandomized incremental construction of the Hausdorff Voronoi diagram of non-crossing clusters
The Hausdorff Voronoi diagram of a set of clusters of points in the plane is a generalization of the classic Voronoi diagram, where distance between a point t and a cluster P is measured as the maximum distance, or equivalently the Hausdorff distance between t and P . The size of the diagram for non-crossing clusters is O(n ), where n is the total number of points in all clusters. In this paper...
متن کاملA Simple RIC for the Hausdorff Voronoi Diagram of Non - crossing Clusters ∗
We present a simplified randomized incremental construction (RIC) for the Hausdorff Voronoi diagram of non-crossing point-clusters. Our algorithm comes in two variants: using a conflict graph and a history graph, respectively. Both variants have O(n log n + k log n log k) expected time complexity and require expected O(n) space, where k is the number of clusters and n is the total number of poi...
متن کاملA Randomized Incremental Approach for the Hausdorff Voronoi Diagram of Non-crossing Clusters
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 while the diagram is defined in a nearest sense. This diagram finds direct applications in VLSI computer-aided design. In this paper, we consider “non-crossing” clusters, for which the combinatorial complexity o...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2004
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-004-1095-0