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.

在本文中，提出了一种最佳并行算法，用于在流行的三维圆环网络上快速计算科学中一个至关重要的基本数值问题，即“前缀和”。提出的并行算法要求在n×n×n三维环面网络的奇数网络尺寸上映射前缀和问题需要总共'4n + 2'个通信动作，而在偶数个偶数网络上进行并行映射需要总共'4n'个通信动作。网络规模。实际上，每个维度从奇数到偶数，再到偶数到奇数网络大小的单位增加导致映射前缀和所需的通信移动分别分别增加2和6个单位。可以将所提出的并行算法的算法性能与基于网格的网络中的对等并行前缀总和方法进行比较。