Summation algorithms on constrained reconfigurable meshes

Abstract

Constrained reconfigurable meshes are one type of parallel computing model which takes the reconfigurability of hardware into account. With these meshes, a practical assumption is given on the communication power such that a signal is propagated through a constant number of processing elements (PEs) say k PEs, at one unit of time. We present algorithms for the fundamental problem of computing the sum of multiple integers. For the problem of summing n binary values, two show an optimal O(n/k)-time algorithm on a constrained reconfigurable mesh of size m/spl times/n, where m=/spl Theta/(log/sup 2/ k/log log k). For the problem of summing n d-bit integers, we present an O((d+/spl radic/dmm)/k) time algorithm on a constrained reconfigurable mesh of size /spl radic/dmn/spl times//spl times//spl radic/dmn.