Scalable algorithms for bichromatic line segment intersection problems on coarse grained multicomputers

Olivier Devillers 1 Andreas Fabri 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n 3 p2, where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of 0(F(n log n log p;p) + T,(n log p, p)), where T,(m, p) is the time used to sort m items on a p processor machine. An additional 0(F(k;p) ) time is spent on the reporting of the k intersections. As the sequential complexity is 0(n log n) and 0(k) for counting and reporting, respectively, we obtain a speedup of F(p;log p) .As a byproduct we present algorithms for the trapezoidal de composition and 1-dimensional range query reporting with the same speedup.
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Olivier Devillers, Andreas Fabri. Scalable algorithms for bichromatic line segment intersection problems on coarse grained multicomputers. [Research Report] RR-1882, INRIA. 1993. ⟨inria-00074791⟩

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