Topological Properties of Hierarchical Interconnection Networks: A Review and Comparison

Hierarchical interconnection networks (HINs) provide a framework for designing networks with reduced link cost by taking advantage of the locality of communication that exists in parallel applications. HINs employ multiple levels. Lower-level networks provide local communication while higher-level networks facilitate remote communication. HINs provide fault tolerance in the presence of some faulty nodes and/or links. Existing HINs can be broadly classified into two classes. those that use nodes and/or links replication and those that use standby interface nodes. The first class includes Hierarchical Cubic Networks, Hierarchical Completely Connected Networks, and Triple-based Hierarchical Interconnection Networks. The second HINs class includes Modular Fault-Tolerant Hypercube Networks and Hierarchical Fault-Tolerant Interconnection Network. This paper presents a review and comparison of the topological properties of both classes of HINs. The topological properties considered are network degree, diameter, cost and packing density. The outcome of this study show among all HINs two networks that is, the Root-Folded Heawood (RFH) and the Flooded Heawood (FloH), belonging to the first HIN class provide the best network cost, defined as the product of network diameter and degree. The study also shows that HFCube(n,n) provide the best packing density, that is, the smallest chip area required for VLSI implementation