Efficient embedding of a hypercube in an irregular WDM network

A heuristic algorithm is presented for efficiently embedding a virtual hypercube into an irregular wavelength division multiplexing (WDM) network so that the message propagation delay is minimized. Embedding a hypercube allows the communications of the many hypercube-base algorithms to map directly to the virtual network. The authors' algorithm optimizes the embedding by effective assignment of virtual addresses as well as the efficient routing of virtual connections. The three-step approach is first based on embedding the irregular graph in a hypercube so that the number of virtual edges that correspond to physical edges is minimized. The routing of the virtual connections and their assignment to logical channels is performed while minimizing the number of wavelengths that must be supported by the WDM system. Experiments with the proposed algorithm show it to produce embeddings with significantly shorter path lengths and requiring fewer wavelengths than previous methods for practical networks.