Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms

Abstract

This paper assumes a parallel RAM (random access machine) model which allows both concurrent reads and concurrent writes of a global memory. The main result is an optimal randomized parallel algorithm for INTEGER_SORT (i.e., for sorting n integers in the range $[1,n]$). This algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. Also given is a deterministic sublogarithmic time algorithm for prefix sum. In addition this paper presents a sublogarithmic time algorithm for obtaining a random permutation of n elements in parallel. And finally, sublogarithmic time algorithms for GENERAL_SORT and INTEGER_SORT are presented. Our sub-logarithmic GENERAL_SORT algorithm is also optimal.