Algebraic properties of some parallel processor interconnection networks

Interconnection networks form an integral part of parallel processing systems, providing the facility for communication between several concurrently executing tasks. This paper presents an algebraic characterization of the sets of communication paths that a network can simultaneously establish between the processing elements of the system. This characterization provides a uniform framework for the analysis of interconnection networks and is shown to yield answers to several important questions concerning the capabilities, limitations and operation of these networks. The networks considered include one way and two way shift register rings, near neighbor meshes, single stage switching networks and briefly, multistage switching networks.