  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.
