Summation algorithms on constrained reconfigurable meshes

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. In this paper, we present algorithms for the fundamental problem of computing the sum of multiple integers. For the problem of summing n binary values, we show an optimal O(n/k)-time algorithm on a constrained reconfigurable mesh of size m × n, where m = Θ (log ² k/log log k). For the problem of summing n d-bit integers, we present an O((d + √dmm)/k)-time algorithm on a constrained reconfigurable mesh of size √ dmn × √ dmn.