Scalable algorithms for bichromatic line segment intersection problems on Coarse Grained Multicomputers

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≥p ², 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 $O(\frac{{n log n log p}}{p} + T_s (n log p,p))$, where T _s(m,p) is the time used to sort m items on a p processor machine. An additional O(k/p) time is spent on the reporting of the k intersections. As the sequential complexity is O(n log n) and O(k) for counting and reporting, respectively, we obtain a speedup of p/log p.

This work was partially supported by the ESPRIT Basic Research Action Nr. 7141 (ALCOM II).