On Higher Order Voronoi Diagrams of Line Segments

  title={On Higher Order Voronoi Diagrams of Line Segments},
  author={Evanthia Papadopoulou and Maksym Zavershynskyi},
We analyze structural properties of the order-k Voronoi diagram of line segments, which surprisingly has not received any attention in the computational geometry literature. We show that order-k Voronoi regions of line segments may be disconnected; in fact a single order-k Voronoi region may consist of Ω(n) disjoint faces. Nevertheless, the structural complexity of the order-k Voronoi diagram of non-intersecting segments remains O(k(n − k)) similarly to points. For intersecting line segments… 
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Farthest line segment Voronoi diagrams
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  • Computer Science, Mathematics
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It is shown that the k-nearest neighbor problem and other seemingly unrelated problems can be solved efficiently with the Voronoi diagram.
Generalization of Voronoi Diagrams in the Plane
The algorithm presented is an improvement of a previous known result which takes $O(Nc^{\sqrt {\log N} } )$ time and is shown to be applicable under a more general metric if certain conditions are satisfied.
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An efficient algorithm for the computation of the segment Voronoi diagram in two dimensions, that uses techniques such as geometric filtering, and experiments that show the robustness, efficiency and scalability of the implementation are presented.
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A new technique is introduced that computes the Voronoi diagram ofX inO(n logn) time, which improves on several previous algorithms for special cases of the problem.
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  • Computer Science
    16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
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The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space, and is used to obtain O(N log N) algorithms for most of the problems considered.
A semidynamic construction of higher-order voronoi diagrams and its randomized analysis
It is proved that a randomized construction of thek-Delaunay tree, and thus of all the order≤k Voronoi diagrams, can be done in O(n logn+k3n) expected time and O(k2n)expected storage in the plane, which is asymptotically optimal for fixedk.
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An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each ofn given line segments in the plane and a purely geometric fact is proved which infers that this description requiresO(n) space to be specified.
Net-Aware Critical Area Extraction for Opens in VLSI Circuits Via Higher-Order Voronoi Diagrams
  • Evanthia Papadopoulou
  • Computer Science
    IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
  • 2011
The approach expands the Voronoi critical area computation paradigm with the ability to accurately compute critical area for missing material defects even in the presence of loops and redundant interconnects spanning over multiple layers.