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All-to-all communication for some wavelength-routed all-optical networks

This paper studies the problem of all-to-all communication for optical networks. In such networks, the vast bandwidth available is utilized through wavelength division multiplexing (WDM): A single physical optical link can carry several logical signals provided that they are transmitted on different wavelengths. In this paper, we consider all-optical (or single-hop) networks, where the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. In this model, we give optimal all-to-all protocols, using minimum numbers of wavelengths, for particular networks of practical interest, namely, the d-dimensional square tori with even sides, the corresponding meshes, and the Cartesian sums of complete graphs.