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Issue RAIRO-Theor. Inf. Appl.
Volume 37, Number 3, July-September 2003
Page(s) 255 - 270
DOI 10.1051/ita:2003019

Theoret. Informatics Appl. 37, 255-270 (2003)
DOI: 10.1051/ita:2003019

On $\mathsf{f}$-wise Arc Forwarding Index and Wavelength Allocations in Faulty All-optical Hypercubes

Ján Manuch1 and Ladislav Stacho2

1  SFU PIMS, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; jmanuch@sfu.ca.
2  Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; lstacho@sfu.ca.


(Received February 4, 2003. Accepted September 15, 2003.)

Abstract
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 f+1 internally node disjoint dipaths connecting all pairs of distinct nodes in the binary r-dimensional hypercube, where $0\le f<r$ . This system of dipaths constitutes a routing protocol that remains functional in the presence of up to f faults (of nodes and/or links). The problem of constructing such protocols for general networks was mentioned in [1]. We compute precise values of f-wise arc forwarding indexes and give (describe dipaths and color them) nearly optimal all-to-all f-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


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