Optimal parallel prefix on mesh architectures

Abstract

Algorithms for efficient implementation of computation of prefix products on mesh-connected processor arrays are presented. Assuming that an arithmetic operation takes unit time and communication/computation ratio for a single input item is T, we show that the prefixes of n items can be computed in time 2T√n + O (log n) on a square mesh with n processors. If n processors are configured as a disc with respect to the Manhattan metric, then the parallel time for the problem becomes √2T√n + O (√T-4√n). We show that both of these algorithms are asymptotically optimal. © 1993, Taylor & Francis Group, LLC. All rights reserved.