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 ≥ 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 (Formula Presented), where Ts(m,p) is the time used to sort m items on a p processor machine. An additional (Formula Presented) 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 (Formula Presented).