A Characterization and Analysis of Parallel Processor Interconnection Networks

The permuting properties of various interconnection networks have been extensively studied. However, not too much attention has been focused on how the permuting properties interact with the mapping of tasks to processors in realizing the communication requirements between tasks. In this paper we focus on characterizing the abilities of some interconnection networks in realizing intertask communication that can be specified as permutations of the task names. From the point of view of the intertask communications requirements, the perceived permuting capabilities may depend upon the specific assignment of tasks to processors. Distinct network permutations may actually result in equivalent intertask communication patterns depending upon the mapping of tasks to processors. Characterizations of networks are developed based upon the theory of permutation groups. A number of properties as well as limitations of these networks become evident from this characterization. Finally, a class of switching networks is identified, that possess many useful properties that make them preferable to multistage interconnection networks in specific applications.