Computational geometry: an introduction
Computational geometry: an introduction
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Farthest-polygon Voronoi diagrams
Computational Geometry: Theory and Applications
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We establish a tight bound on the worst-case combinatorial complexity of the farthest-color Voronoi diagram of line segments in the plane. More precisely, given k sets of total n line segments, the combinatorial complexity of the farthest-color Voronoi diagram is shown to be Θ(kn+h) in the worst case, under any Lp metric with 1≤p≤∞, where h is the number of crossings between the n line segments. We also show that the diagram can be computed in optimal O((kn+h)logn) time under the L1 or L∞ metric, or in O((kn+h) (α(k) logk+logn)) time under the Lp metric for any 1