Fault-Tolerant Wavelength Allocations in All-optical Hypercubes

Motivated by wavelength division multiplexing in all-optical networks, we consider the problem of finding an optimal (with respect to the least possible number of wavelengths) set of f +1 internally node disjoint dipaths for every pair of distinct nodes in the binary r-dimensional hypercube, where 0 f < r. This system of dipaths serves as a routing protocol that remains functional in the presence of up to f faults (nodes and/or links) in the hypercube. The importance of such protocols follows from the fact that the major applications for all-optical networks require connections that last for relatively long periods once set up. In this model, we give nearly optimal All-to-All protocols, in terms of number of wavelengths, for the hypercube network.