A class of hierarchical graphs as topologies for interconnection networks

We study some topological and algorithmic properties of a recently defined hierarchical interconnection network, the hierarchical crossed cube H C C ( k , n ) , which draws upon constructions used within the well-known hypercube and also the crossed cube. In particular, we study: the construction of shortest paths between arbitrary vertices in H C C ( k , n ) ; the connectivity of H C C ( k , n ) ; and one-to-all broadcasts in parallel machines whose underlying topology is H C C ( k , n ) (with both one-port and multi-port store-and-forward models of communication). Moreover, some of our proofs are applicable not just to hierarchical crossed cubes but to hierarchical interconnection networks formed by replacing crossed cubes with other families of interconnection networks. As such, we provide a generic construction with accompanying generic results relating to some topological and algorithmic properties of a wide range of hierarchical interconnection networks