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Efficient Geometric Algorithms on the EREW PRAM
January 1995 (vol. 6 no. 1)
pp. 41-47

Abstract—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 $O(\log n)$ time using $O(n/\log n)$ EREW PRAM processors, where $n$ 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 $O(\log n)$ time and using $O(n/\log n)$ processors) only on the CREW PRAM, which is a stronger model than the EREW PRAM.

Index Terms—Computational geometry, convex hulls, kernel, parallel algorithms, parallel random access machines, read conflicts, simple polygons, triangulation, visibility.

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Danny Z. Chen, "Efficient Geometric Algorithms on the EREW PRAM," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 1, pp. 41-47, Jan. 1995, doi:10.1109/71.363412
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