Degree of scalability: scalable reconfigurable mesh algorithms for multiple addition and matrix-vector multiplication

摘要

The usual concern when scaling an algorithm on a parallel model of computation is preserving efficiency while increasing or decreasing the number of processors. Many algorithms for reconfigurable models, however, attain constant time at the expense of an inefficient algorithm. For these algorithms, scaling down the number of processors while preserving inefficiency is no benefit once constant time execution is lost. In fact, one can often accelerate the efficiency of these algorithms while reducing the number of processors. To quantify this improvement in efficiency, this paper introduces the measure of degree of scalability to complement the insight obtained from efficiency for such algorithms. Demonstrating the utility of this measure, we present new reconfigurable mesh (R-Mesh) algorithms for multiple addition and matrix-vector multiplication, improving both the number of processors and the degree of scalability compared to previous algorithms. We also extend these results to floating point number operands, which have previously received little attention on the R-Mesh.