Efficient protocols for permutation routing on all-optical multistage interconnection networks

To realize a routing request R on a WDM (wavelength division multiplexing) all-optical network, one needs to set up routing paths in the network for every input-output pair in R and to assign a wavelength to each path so that the paths with the same wavelength are edge-disjoint. The optical bandwidth of the WDM all-optical network is the number of wavelengths supported by each link of the network. If the number of wavelengths for realizing R is at most the bandwidth of the network then R can be routed in one round of routing. However, when the number of wavelengths needed is beyond the bandwidth, multiple rounds of routing are required. In this case, it is important to minimize the number of rounds of routing. We give two deterministic algorithms for permutation routings on the parallel computing systems connected by all-optical multistage interconnection networks (MINs). For the parallel computing systems with practical size, the first algorithm realizes any permutation in two rounds of routing. The second algorithm realizes any bit-permute-complement (BPC) permutation on the n-dimensional MINs in two rounds of routing