On the Efficient Summation of N Numbers on an N-Processor Reconfigurable Mesh

A reconfigurable mesh is a two-dimensional processor array equipped with a reconfigurable bus system that can be changed dynamically to suit different computational needs. In this paper we present a parallel algorithm for the summation of N numbers each in the range [0, 2b). The algorithm runs in O(b+log log N) time on reconfigurable mesh. This is an improvement over the best previously known algorithm that solves the same problem in O(b log log N) time. The algorithm is finally extended to compute the prefix sums of the given numbers in the same time.