Linear Recursive Networks and Their Applications in Distributed Systems

We present a new class of interconnection topologies called the Linear Recursive Networks (LRNs) and examine their possible applications in distributed systems. Each LRN is characterized by a recursive pattern of interconnection which can be specified by simple parameters. Basic properties such as node degree, diameter, and the performance of routing algorithms for all LRNs are then collectively analyzed in terms of these parameters. By choosing appropriate values for the parameters, our results can assist a network designer in selecting a topology with required routing performance and cost of interconnection. A subclass of LRNs, called Congruent LRNs (CLRNs), is also identified here and shown to possess desirable properties for more tightly coupled systems. It is shown that the CLRNs include existing networks such as hypercube and generalized Fibonacci cubes. These results suggest that the linear recursive networks potentially have applications in interconnecting distributed systems.