Optimal Parallel Prefix Sum Computation on Three-Dimensional Torus Network

Abstract

In this article, an optimal parallel algorithm is suggested for fast computation of a crucial yet fundamental numerical problem in science named ‘prefix sum’ on a popular three-dimensional torus network. The proposed parallel algorithm demands total ‘4n + 2’ communication moves for mapping prefix sum problem on odd network sizes of n × n×n three-dimensional torus network, whereas total ‘4n’ communication moves is required for parallel mapping of same on even network sizes. In fact, a unit increase in each dimension from odd to even and even to odd network sizes resulted in the constant increase of 2 and 6 units, respectively, in the required communication moves for mapping prefix sum. The algorithmic performance of the proposed parallel algorithm can be compared to counter-part parallel prefix sum approaches on grid-based networks.