The Complexity of Data Reduction on a Reconfigurable Linear Array

We consider the basic problem of gathering information dispersed among the nodes of a reconfigurable linear array. An upper and a matching lower bound are obtained for data-reduction operations, including, for example, the computation of several independent sums of input sets which are each given at a network node. Simulations of linear arrays by other networks are presented, thus applying linear array algorithms as upper bounds for these networks, too. The complexity analysis introduces a novel criteria for the efficiency of reconfigurable network algorithms, namely the bus-usage. The bus-usage measures the utilization of the network communication links by the algorithm. The analysis show that there is a trade-off between the running time of an algorithm and its bus-usage.