F. Dehne and R. Klein, \The Big Sweep: On the Power of the Wavefront Approach to Voronoi Diagrams, " Algorithmica, 17:19-32, 1997. Home/Search Document Details and Download
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Critical Area Computation - A New Approach - Papadopoulou, Lee (1999) (2 citations) (Correct)
....of n rectangles (see Figure 9) We consider rectangles instead of rectilinear polygons for simplicity of presentation; the same algorithm can be easily generalized to rectilinear layouts. The time complexity is O(n log n) and it is based on the wavefront paradigm introduced by Dehne and Klein [3] for the Voronoi diagram of points. s s L spike event wavefront Figure 10: Construction of the Voronoi diagram by plane sweep method. We shall apply a vertical sweep line L sweeping across the entire plane from left to right. The set of rectangles at any instant of the sweeping process will be ....
.... status is also O(n) The operation associated with each event point 0 R Figure 14: 2nd Order Voronoi diagram in the Voronoi cell of R takes O(log n) time, giving rise to an overall time complexity of O(n log n) The correctness of the algorithm follows from the result of Dehne and Klein[3]. 2 Once the Voronoi diagram is available we can compute the 2nd order subdivision within each Voronoi cell in a similar fashion. Figure 14, shows the 2nd order partitioning in the Voronoi cell of the middle rectangle R 0 . The Voronoi cell of R 0 is shown shaded. The partitioning line segments ....
F. Dehne and R. Klein, "The Big Sweep: On the power of the Wavefront Approach to Voronoi Diagrams," Algorithmica(1997), 17, 19-32.
Proximity Problems for Time Metrics Induced by the .. - Abellanas.. (2001) Self-citation (Klein) (Correct)
....D t (p; q) is an unbounded connected region. Hence, B t (p; q) is a curve homeomorphic to (0; 1) Furthermore, two of these curves can only intersect at most a nite number of connected components. Hence, property (v) holds too. 2 As a consequence of this theorem, the sweep line algorithm in [4] can be used for computing the Voronoi Diagram, and we get the following result. Corollary 6 The Voronoi Diagram of a set of n points with respect to the time distance can be computed in O(n log n) time and linear space. L p 1 p 3 p 2 Figure 3: Time Voronoi Diagram for points p 1 ; p 2 and p 3 . ....
F. Dehne, R. Klein, "The big sweep: On the Power of the Wavefront Approach to Voronoi Diagrams", Algorithmica, Vol. 17, pp.19-32, 1997.
Robustness of Algorithm for k-Gon Voronoi Diagram Construction - Chen, Xu (2002) (Correct)
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F. Dehne and R. Klein, \The Big Sweep: On the Power of the Wavefront Approach to Voronoi Diagrams, " Algorithmica, 17:19-32, 1997.
Robustness of Algorithm for k-Gon Voronoi Diagram Construction - Chen, Papadopoulou, Xu (Correct)
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F. Dehne and R. Klein, \The Big Sweep: On the Power of the Wavefront Approach to Voronoi Diagrams, " Algorithmica, 17:19-32, 1997.
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