Optimal Parallel Algorithms for Selection, Sorting and Computing Convex Hulls

Abstract

Parallel algorithms are described for three problems that are often to be solved in computational geometry, namely selection, sorting and computing convex hulls. For a problem of size n, all three algorithms use n 1-e processors where 0<e<1 and depends on the number of available processors. The cost of each of the algorithms, i.e. the number of processors multiplied by the worst-case running time, matches an existing lower bound on the number of operations required in the worst case to solve the given problem and is therefore optimal to within a constant factor.