Transpose on vertex symmetric digraphs

We discuss transpose (sometimes called universal exchange or all-to-all) on vertex symmetric networks. We provide a method to compare the efficiency of transpose schemes on two different networks with a cost function based on the number processors and wires needed to complete a given algorithm in a given time.

Network routing on regular directed graphs from spanning factorizations

Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, universal broadcast, universal summation) that can be critical tasks when complex algorithms are mapped to parallel machines. We showed that utilizing the symmetry can make network optimization a tractable problem. In particular, we showed that Cayley graphs have the desirable property that certain routing schemes starting from a single node can be transferred to all nodes in a way that does not introduce conflicts. In this paper, we define the concept of spanning factorizations and show that this property can also be used to transfer routing schemes from a single node to all other nodes. We show that all Cayley graphs and many (perhaps all) vertex transitive graphs have spanning factorizations.

Automorphisms of the cycle prefix digraph

Cycle prefix digraphs have been proposed as an efficient model of symmetric interconnection networks for parallel architecture. It has been discovered that the cycle prefix networks have many attractive communication properties. In this paper, we determine the automorphism group of the cycle prefix digraphs. We show that the automorphism group of a cycle prefix digraph is isomorphic to the symmetric group on its underlying alphabet. Our method can be applied to other classes of graphs built on alphabets including the hypercube, the Kautz graph,and the de Bruijn graph.