Elena Khramtcova

  • Citations Per Year
Learn More
Stabbing a set S of n segments in the plane by a line is a well-known problem. In this paper we consider the variation where the stabbing object is a circle instead of a line. We show that the problem is tightly connected to two cluster Voronoi diagrams, in particular, the Hausdorff and the farthest-color Voronoi diagram. Based on these diagrams, we provide(More)
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 non-crossing clusters in the plane, for which the(More)
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(More)
We present linear-time algorithms to construct tree-structured Voronoi diagrams, after the sequence of their regions at infinity or along a given boundary is known. We focus on Voronoi diagrams of line segments, including the farthest-segment Voronoi diagram, the order-(k+1) subdivision within a given order-k Voronoi region, and deleting a segment from a(More)
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,(More)
Consider a pair of plane straight-line graphs whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n logn)-time O(n)-space technique to preprocess such a pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number(More)
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(More)
  • 1