Constructing integral uniform flows in symmetric networks with application to the edge-forwarding index problem

We study the integral uniform (multicommodity) flow problem in a graph G and construct a fractional solution whose properties are invariant under the action of a group of automorphisms Γ < Aut(G). The fractional solution is shown to be close to an integral solution (depending on properties of Γ), and in particular becomes an integral solution for a class of graphs containing Cayley graphs. As an application we estimate asymptotically (up to additive error terms) the edge congestion of an optimal integral uniform flow (edge forwarding index) in the cube connected cycles and the butterfly. The research of the first author was supported by NSF grant CCR-9528228. Research of the second author was supported in part by the Hungarian NSF contracts T 016 358 and T 019 367, and by the NSF contract DMS 97