An O(n Log N) Algorithm for the Voronoi Diagram of a Set of Simple Curve Segments: Preliminary Version (Classic Reprint) - Hardcover

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Excerpt from An O(n Log N) Algorithm for the Voronoi Diagram of a Set of Simple Curve Segments: Preliminary Version

We overcome this problem by computing only the 'essential' part of the Voronoi diagram of a slab, where this essential part has size only O(k) if the slab contains 1: endpoints of X. Furthermore, merging two slabs that collectively contain 1: endpoints takes only O(k) work. (note: actually, I: should be the number of segments with endpoints in the slab.) This implies that cad-i stage takes linear time and our stated time bound follows.

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