Abstract
In this paper, we present an O \( O\left( {\frac{1} {\alpha }\log n} \right) \) log n) (for any constant 0 ≤α≤1) time parallel algorithm for constructing the constrained Voronoi diagram of a set L of n non-crossing line segments in E 2, using O(n 1+α) processors on a CREW PRAM model. This parallel algorithm also constructs the constrained Delaunay triangulation of L in the same time and processor bound by the duality.
Our method established the conversions from finding the constrained Voronoi diagram L to finding the Voronoi diagram of S, the endpoint set of L. We further showed that this conversion can be done in O(log n) time using n processors in CREW PRAM model. The complexity of the conversion implies that any improvement of the complexity for finding the Voronoi diagram of a point set will automatically bring the improvement of the one in question.
This work is supported by NSERC grant OPG0041629.
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Chin, F., Lee, D.T., Wang, C.A. (1999). A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_24
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DOI: https://doi.org/10.1007/3-540-48447-7_24
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