Issue No. 01 - January (1995 vol. 6)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.363412
<p><it>Abstract—</it>We present a technique that can be used to obtain efficient parallel geometric algorithms in the EREW PRAM computational model. This technique enables us to solve optimally a number of geometric problems in <math><tmath>$O(\log n)$</tmath></math> time using <math><tmath>$O(n/\log n)$</tmath></math> EREW PRAM processors, where <math><tmath>$n$</tmath></math> is the input size of a problem. These problems include: computing the convex hull of a set of points in the plane that are given sorted, computing the convex hull of a simple polygon, computing the common intersection of half-planes whose slopes are given sorted, finding the kernel of a simple polygon, triangulating a set of points in the plane that are given sorted, triangulating monotone polygons and star-shaped polygons, and computing the all dominating neighbors of a sequence of values. PRAM algorithms for these problems were previously known to be optimal (i.e., in <math><tmath>$O(\log n)$</tmath></math> time and using <math><tmath>$O(n/\log n)$</tmath></math> processors) only on the CREW PRAM, which is a stronger model than the EREW PRAM.</p><p><it>Index Terms—</it>Computational geometry, convex hulls, kernel, parallel algorithms, parallel random access machines, read conflicts, simple polygons, triangulation, visibility.</p>
D. Z. Chen, "Efficient Geometric Algorithms on the EREW PRAM," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 41-47, 1995.