Abstract
We address the issue of efficiently assigning wavelengths to communication requests in wavelength division multiplexing (WDM) optical networks. We consider directed tree and tree of rings topologies. These are topologies of concrete practical relevance for which undirected underlying graph models have been studied by Raghavan and Upfal [6]. Directed models were first studied by Mihail et al [4].
For trees, we give a polynomial time routing algorithm that, for requests of maximum load L per directed fiber link, uses at most 7/4L wavelengths. This improves the bound of Mihail et al.. As a corollary we also give an algorithm for trees of rings that uses 7/2L wavelengths.
Partially supported by Progetto MURST 40%, Algoritmi, Modelli di Calcolo e Strutture Informative and by EU Esprit Project GEPPCOM.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswani, B. Shieber, and M. Sudan, Efficient Routing and Scheduling Algorithms for Optical Networks, in Proc. of SODA 93.
J.-C. Bermond, L. Gargano, S. Perennes, A. A. Rescigno, and U. Vaccaro, Efficient Collective Communication in Optical Networks, to appear in Proc. of ICALP 96.
P. E. Green, Fiber Optic Communication Networks, Prentice Hall, 1992.
M. Mihail, C. Kaklamanis, and S. Rao, Efficient Access to Optical Bandwidth, in Proc. of FOCS 1995.
D. Minoli, Telecommunications Technology Handbook, Artech House, 1991.
P. Raghavan and E. Upfal, Efficient Routing in All-Optical Networks, in Proc. of STOC 1994.
W. Aiello, S. Rajagopalan, R. Venkatesan, Design of practical and Provably Good Random Number Generators, Proc. ACM-SIAM Symposium on Discrete Algorithms SODA 1995, to appear.
Alexander, Bondurant, Byrne, Chan, Finn, Gallager, Glance, Haus, Humblet, Jain, Kaminiw, Karol, Kennedy, Kirby, Le, Saleh, Schofield, Shapiro, Shankar, Thomas, Williamson and Milson, A Precompetitive Consortium on Wide-Band All-Optical Networks, IEEE J. of Lightwave Technology, Vol 11 No 5/6, 1993, pp 714–735.
C. Berge, Graphs and Hypergraphs, North-Holland Library, 1970.
G.K. Chung et al, ONTC-ARPA Technology Development Group, Experimental Demonstration of a Reconfigurable WDM/ATM/SONET Multiwavelength Network Testbed, OFC Optical Fiber Conference, San Jose CA, January 1993.
A. Frank, Edge-disjoint Paths in Planar Graphs, JCTB 39, 1985, pp 164–178.
M. Garey, D. Johnson, G. Miller, and C. Papadimitriou, The Complexity of Coloring Circular Arcs and Chords, SIAM J. Alg. Disc. Math., Vol 1, No 2, 1980, pp 216–227.
M. Goldberg, Edge-Coloring of Multigraphs: Recoloring Technique, Journal of Graph Theory, Vol 8, 1984, pp 123–137.
M. Goldberg, An Approximate Algorithm for the Edge-Coloring Problem, Congressus Numerantium, Vol 43, 1984, pp. 317–319.
I. Holyer, The NP-Completeness of Edge-Coloring, SIAM J. Comp., Vol 10, No 4 1981, pp 718–720.
B. Lennon, High Speed Optical Links between Livermore and Berkeley, Advanced Telecommunications Program of LLNL, ONTC Presentation, Redbank, New Jersey, November 1994.
ONTC-ARPA, Brackett, Acampora, Sweitzer, Tangonan, Smith, Lennon, Wang, Hobbs, A Scalable Multiwavelength Multihop Optical Network: A Proposal for Research in All-Optical Networks, IEEE J. of Lightwave Technology, Vol 11 No 5/6, 1993, pp 736–753. OK
ONTC-ARPA Network Studies Group, Lu, Roorda, Coathup, Gruber, Ashton, Leeson, Boutilier: BNR/Northern Telecom, Bala, Brackett, Cordell, Goldstein, Goodman, Chung, Mihail, Winkler: Bellcore, Acampora, Stern, Zhang, Kovaacevic, Brown, Guo, Jagannath, Jiang: Columbia University, Final Phase I Report, August 1994, pp 25–76.
R. Pankaj, Architectures for Linear Lightwave Networks, Ph.D. Thesis, Department of Electrical Engineering and Computer Science, MIT, Cambridge MA, 1992.
A. Schrijver, Edge-disjoint Paths in Directed Planar Graphs, SIAM Journal of Algorithms, to appear.
A. Tucker, Coloring a Family of Circular Arcs, SIAM J. Appl. Math. Vol 29, No 3, 1975, pp 493–502.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaklamanis, C., Persiano, P. (1996). Efficient wavelength routing on directed fiber trees. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_75
Download citation
DOI: https://doi.org/10.1007/3-540-61680-2_75
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61680-1
Online ISBN: 978-3-540-70667-0
eBook Packages: Springer Book Archive