Routing and embeddings in cyclic Petersen networks: an efficient extension of the Petersen graph

The Petersen graph is a Moore graph that has node degree 3, diameter 2, and optimal network size 10. In this paper, we present a class of interconnection networks, called cyclic Petersen networks (CPNs), which efficiently extend the Petersen graph to obtain larger networks with small diameter and node degree. We derive balanced routing algorithms and efficient embeddings for CPNs. In particular, we show that many normal mesh algorithms can be emulated on CPNs with a slowdown factor of about 1.1. We also show that complete CPNs can embed meshes, tori, meshes of trees, and folded Petersen networks with dilation 3, hypercubes and generalized hypercubes with dilation 4, and pyramids with dilation 5.