On the Multiplexing Degree Required to Embed Permutations in a Class of Networks with Direct Interconnects

There are two approaches for establishing a connection in a network whose links are multiplexed with virtual channels. One is called Path Multiplexing (PM), in which the same channel has to be used on each link along a path, and the other is Link Multiplexing (LM), in which diierent channels may be used. We study the problem of embedding permutations in PM and LM, and in particular, determine the threshold (minimal) multiplexing degree needed for a network to be rearrangeably nonblocking. We found that PM and LM are equally eeective in linear arrays, and LM is slightly more eeective than PM in rings, meshes, tori and hypercubes. Our results suggest that PM may be more cost-eeective in implementing networks with multiplexed optical interconnects.