An efficient method for representing and transmitting message patterns on multiprocessor interconnection networks

Abstract

We describe a formalism for representing address sets, and for representing message patterns for multiprocessor interconnection networks. In this formalism a descriptor called a mask is used to represent a set of equal length bit vectors. Such a set can be interpreted as a set of processor addresses, or as a set of messages. We focus on the implications that this formalism has for routing message patterns on bundled omega networks. Specifically, we show that when a message pattern is represented in this formalism, a number of properties of the message pattern can be determined in polynomial time. This includes such things as determining whether the message pattern contains congestion. In addition, we show that the formalism defines a subclass of message patterns for which the minimum round partitioning problem, which in general is NP-hard, is solvable in linear time. We show this result to be true for both broadcast and non-broadcast bundled omega networks. This generalizes a known result for bit-permute-complement permutations to a more general class of message patterns, and to a larger class of networks.