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On ƒ-wise Arc Forwarding Index and Wavelength Allocations in Faulty All-optical Hypercubes

Published online by Cambridge University Press:  15 November 2003

Ján Maňuch  and
Ladislav Stacho
Ján Maňuch
Affiliation:
SFU PIMS, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; jmanuch@sfu.ca.
Ladislav Stacho
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; lstacho@sfu.ca.
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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 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 [1]. 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].

Keywords

All-optical networksfault tolerant systemforwarding indexoptical indexhypercube.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 3 , July 2003 , pp. 255 - 270
Copyright
© EDP Sciences, 2003

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References

Beauquier, B., All-to-all communication for some wavelength-routed all-optical networks. Networks 33 (1999) 179-187. 3.0.CO;2-6>CrossRef
B. Beauquier, C.J. Bermond, L. Gargano, P. Hell, S. Perennes, and U. Vaccaro, Graph Problems arising from wavelength-routing in all-optical networks, in Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, (1997).
Beauquier, B., Hell, P. and Pérennes, S., Optimal wavelength-routed multicasting. Discrete Appl. Math. 84 (1998) 15-20. CrossRef
J.-C. Bermond, L. Gargano, S. Perennes, A. Rescigno and U. Vaccaro, Efficient collective communications in optical networks, in: Proc. 23rd ICALP'96, Paderborn, Germany, Lecture Notes in Comput. Sci. 1099 (1996) 574-585.
N.K. Cheung, K. Nosu and G. Winzer (eds.), Dense wavelength division multiplexing techniques for high capacity and multiple access communication systems. J. Selected Areas in Commun. 8 (1990).
T. Erlebach and K. Jansen, Scheduling of virtual connections in fast networks, in Proc. 4th Workshop on Parallel Systems and Algorithms PASA'96, 13-32.
Gargano, L., Hell, P. and Pérennes, S., Colouring paths in directed symmetric trees with applications to optical networks, J. Graph Theory 38 (2001) 183-186. CrossRef
R.L. Graham, D.E. Knuth and O. Patashnik, Concrete mathematics: a foundation for computer science. Addison-Wesley (1989).
P.E. Green, Fiber Optic Networks. Prentice Hall (1993).
Lam, C.C., Huang, C.H. and Sadayappan, P., Optimal algorithms for all-to-all personalized communication on rings and two dimensional tori. J. of Parallel and Distributed Comput. 28 (1997) 3-13. CrossRef
Manoussakis, Y. and Tuza, Z., The forwarding index of directed networks. Discrete Appl. Math. 68 (1996) 279-291. CrossRef
Manuch, J. and Stacho, L., Fault-tolerant wavelength allocation in all-optical hypercubes, in Proc. 6th SIROCCO, Informatics 5 (1999) 219-232.
D. Minoli, Telecommunications Technology Handbook. Artech House (1991).
R.K. Pankaj, Architectures for linear light-wave networks. Ph.D. Thesis, Dep. of Electrical Engineering and Computer Science, MIT, Cambridge, MA (1992).
Pankaj, R.K. and Gallager, R.G., Wavelength requirements of all-optical networks. IEEE/ACM Trans. Network. 3 (1995) 269-280. CrossRef
H. Shröder, O. Sýkora and I. Vrto, Optical all-to-all communication for some product graphs, in Proc. 24th SOFSEM'97, Lecture Notes in Comput. Sci. 1338 (1997) 555-562.
G. Wilfong, Minimizing wavelengths in an all-optical ring network, in Proc. ISAAC'96 Lecture Notes in Comput. Sci. 1178 (1996) 346-355.