On ƒ-wise Arc Forwarding Index and Wavelength Allocations in Faulty All-optical Hypercubes
SFU PIMS, Simon Fraser University,
8888 University Drive, Burnaby BC, V5A 1S6 Canada;
2 Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; firstname.lastname@example.org.
Accepted: 15 September 2003
Motivated by the 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 ƒ+1 internally node disjoint dipaths connecting all pairs of distinct nodes in the binary r-dimensional hypercube, where 0 ≤ ƒ < r. This system of dipaths constitutes a routing protocol that remains functional in the presence of up to ƒ faults (of nodes and/or links). The problem of constructing such protocols for general networks was mentioned in . We compute precise values of ƒ-wise arc forwarding indexes and give (describe dipaths and color them) nearly optimal all-to-all ƒ-fault tolerant protocols for the hypercube network. Our results generalize corresponding results from [1, 4, 14].
Mathematics Subject Classification: 68M10 / 68M15 / 68R05
Key words: All-optical networks / fault tolerant system / forwarding index / optical index / hypercube.
© EDP Sciences, 2003