Hypercycles: a status report

Abstract

The authors present the Hypercycles, a class of multidimensional graphs, which are generalizations of the n-cube. These graphs are obtained by allowing each dimension to incorporate more than two elements and a cycle interconnection strategy. Hypercycles offer simple routing and the ability, given a fixed degree, to choose among a number of alternative size graphs. These graphs can be used in the design of interconnection networks for distributed systems tailored specifically to the topology of a particular application. A backtrack-to-the-origin-and-retry routing scheme in which paths that block at intermediate nodes are abandoned and a new attempt is made is presented. Intermediate nodes are chosen at random at each point from among the ones that form the shortest paths from a source to a destination. Simulation results that establish the performance of a variety of configurations are presented. In addition, the initial attempt at constructing a Hypercycle-based router is discussed.<>