The index-permutation graph model for hierarchical interconnection networks

In this paper, we present the index-permutation (IP) graph model, and apply it to the systematic development of efficient hierarchical networks. We derive several classes of interconnection networks based on IP graphs to achieve desired properties; the results compare favorably with popular interconnection networks, as measured by topological (e.g., node degree and diameter) and algorithmic properties, and are particularly efficient in view of their sparse inter-module communication patterns. In particular, the diameters of suitably-constructed super-IP graphs, a subclass of IP graphs, are optimal within a factor of 1+o(1), given their node degrees. The IP graph model can also be used as a common platform that unifies the architectures and algorithms for a vast variety of interconnection networks