Embedding of meshes on rotator graphs

A set of directed permutation graphs called rotator graphs were proposed as an alternative to the star and pancake graphs for multiprocessor interconnection networks. The rotator graphs have a smaller diameter than star and pancake graphs for the same number of nodes, while sharing the properties of star, pancake, and binary hypercubes like maximal fault tolerance, partitionability, etc. In this paper we develop a class of algorithms for recognizing undirected mesh structures in n-rotator graphs. The average dilation of the embeddings are very low as compared to the dilation of the embedding. These embeddings will be very useful for regular computations with bi-directional requirements, in addition to the irregular computations in n-rotator graphs. Most of the results presented here equally apply to another set of directed Cayley graphs, the cycle prefix digraphs