An optimal multiple bus network for fan-in algorithms

Abstract

We consider a class of algorithms called fan-in algorithms, with numerous applications in problems involving semigroup operations. We present a multiple bus network (MBN) that runs any fan-in algorithm in optimal number of steps. The degree and loading of this MBN are each 3. We prove that the product of the degree and loading of any MBN that runs a fan-in algorithm in optimal time is at least 9. This establishes the proposed MBN to be optimal.