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All-Optical Network Topologies Based on Expander Graphs

All-optical networks are networks for which all data paths remain optical from input to output. We discuss a class of wavelength division multiple access (WDMA) networks that are homogeneous in the sense that each node contains both an input/output port and a switch. We focus on permutation routing problem and first present a lower bound on the number of wavelengths required for permutation routing as a function of the size and degree of the network. We then use a network topology based on expander graphs and derive an expression for the number of wavelengths that are sufficient for the permutation routing problem. We present these numbers as asymptotic upper bounds for very large networks.