A theory of decomposition into prime factors of layered interconnection networks

The \Cross Product" technique introduced by Even and Litman EL92] is extended into a full decomposition theory enabling a unique (up to isomorphism) and polynomial factorization of layered interconnection networks (including most well-known networks) into a product of prime factors. A polynomial algorithm is provided for checking whether a given layered interconnection network is isomorphic to a uniquely decomposible network into prime factors.