Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T19:03:06.690Z Has data issue: false hasContentIssue false
  • English
  • Français

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; [email protected].
Ladislav Stacho
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC, V5A 1S6 Canada; [email protected].
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.