Some parallel sorts on a mesh-connected processor array and their time efficiency

Abstract

For each value to be sorted in the process of the parallel bubble sort computation, we evaluate the exact time necessary to route the value to its final position. Using this evaluation we design some efficient parallel sorting algorithms that can be implemented on a mesh-connected processor array and analyze their time complexities. Our algorithms are some combinations of the parallel bubble sorts in different directions, and their control hardware is very simple. Although the time complexities of our algorithms are O(N 1 2 log N) , they are as fast as the implementations of Batcher's bitonic sort and odd-even merge sort on the mesh-connected processor array for practical values of N, 1 ≤ N ≤ 128 2. We also show a parallel sort that is very fast in the average case for practical values of N, 1 ≤ N ≤ 128 2.