Multicomputer interconnection network based on a star graph

Abstract

An interconnection network based on a star graph of arbitrary order n, is analysed. Star graphs belong to a family of Cayley graphs, in which vertices correspond to elements of a permutation group, and edges correspond to generators of the group. Generators of the star graph of order n are n-1 transpositions, which may be represented with a star transposition tree. The algebraic properties of these graphs are investigated through analysis of the corresponding transposition tree. The algebraic expression for the shortest path between two nodes is found, and it is shown that every shortest path consists of a number of subpaths, which may be combined in an arbitrary order. From the analysis of shortest paths follows the minimum number of virtual channels, into which every physical channel must be split in order to avoid deadlock. Finally, a routing algorithm is developed which repetitively extracts subpaths, by sorting the source permutation to the destination permutation.