Abstract
This paper surveys theoretical results for wavelength—routing in all—optical networks and presents several open problems. We focus our attention on graph-theoretical problems and proof techniques.
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References
A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswami, B. Schieber, M. Sudan, “Efficient Routing and Scheduling Algorithms for Optical Networks”, Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms SODA’94, 1994, 412–423.
R. Ahlswede, L. Gargano, H.S. Haroutunian, L.H. Khachatrian, “Fault—Tolerant Minimum Broadcast Networks”, NETWORKS,27, 1996, 293307.
N. Alon, “Eigenvalues and Expanders”, Combinatorica, 6, 1986, 83–96.
V. Auletta, I. Caraggiannis, C. Kaklamanis, G. Persiano, “Efficient Wavelength Routing with Low—Degree Converters”, Proceedings of DIMACS Workshop on Optical Networks, 1998.
L. A. Bassalygo, “Asymptotically Optimal Switching Circuits, Problems of Information Transmission, 1981, 206–211.
B. Beauquier, “All-to-All Communication in Some Wavelength-Routed All—Optical Networks”, INRIA Research Report,3452.
B. Beauquier, P. Hell, S. Perennes, “Optimal Wavelength-Routed Multi-casting”, Discr. Appl. Math 84, 1998, 15–20.
B. Beauquier, J.-C. Bermond, L. Gargano, P. Hell, S. Perennes, and U. Vaccaro, “Graph Problems Arising from Wavelength—Routing in All—Optical Networks”, 2nd Workshop on Optics and Computer Science WOCS,Geneve, Switzerland, 1997
C. Berge, Graphs,North—Holland.
J.-C. Bermond, N. Homobono, and C. Peyrat, “Large Fault—Tolerant Interconnection Networks”, Graphs and Combinatorics 5, 1989, 107–123.
J.—C.. Bermond, L. Gargano, S. Perennes, A.A. Rescigno, U. Vaccaro, “Efficient Collective Communication in Optical Networks”, Proceedings of 23th International Colloquium on Automata, Languages, and Programming ICALP 96, LNCS, 1099, Springer-Verlag, 1996, 574–585.
F.R.K. Chung, Spectral Graph Theory, CBMS 92, American Mathematical Society, 1997.
T. Erlebach and K. Jansen. “Scheduling of Virtual Connections in Fast Networks”, Proc. of 4th Workshop on Parallel Systems and Algorithms PASA ‘86, 1996, 13–32.
L. Gargano, “Limited Wavelength Conversion in All-Optical Tree Networks”, Proceedings of 25th International Colloquium on Automata, Languages, and Programming ICALP 98, Aalborg, 1998.
L. Gargano, P. Hell, S. Perennes, “Colouring All Directed Paths in a Symmetric Tree with Applications to WDM Routing”, Proceedings of 24th International Colloquium on Automata, Languages, and Programming ICALP 97, P. Degano, R. Gorrieri, A. Marchetti—Spaccamela Eds, LNCS, 1256, Springer-Verlag, 1997, 505–515.
O. Gerstel, S. Kutten, R. Ramaswami and G. Sasaki, “Wavelength Conversion in All-Optical Ring Networks”, Proceedings of 6th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing PODC’97, 1997.
M. C. Golumbic and R. E. Jamison. “The Edge Intersection Graphs of Paths in a Tree”, Journ. Comb. Theo., Series B, 38, 1985, 8–22.
M. C. Golumbic and R. E. Jamison. “Edge and Vertex Intersection of Paths in a Tree”, Discrete Mathematics, 55, 1985, 151–159.
P. E. Green, Fiber-Optic Communication Networks, Prentice—Hall, 1992.
P. E. Green, “Optical Networking Update”, IEEE J. Selected Areas in Comm., vol. 14, 1996, 764–779.
M. C. Heydemann, J-C. Meyer arid D. Sotteau, “Orr Forwarding Indices of Networks”, Discrete Applied Mathematics 23, 1989, 103–123.
K. Kaklamanis G. Persiano, T. Erlebach, K. Jansen, “Constrained Bipartite Edge Coloring with Applications to Wavelength Routing” Proceedings of 24th International Colloquium on Automata, Languages, and Programming ICALP 97, Bologna, Italy, 1997.
I.A. Karapetian, “On Coloring of Arc Graphs”, Dokladi of the Academy of Science of the Armenian SSR, 70 (5), 1980, 306–311.
R. Klasing, “Methods and Problems of Wavelength—Routing in All—Optical Networks”, Proceedings of 23rd International Symposium on Mathematical Foundations of Computer Science MFSC’98, 1998, LNCS 1450.
J. Kleimberg, E. Kumar, “Wavelength Conversion in Optical Networks”, Proceedings of SODA’99, 1999.
V. Kumar, “Approximating Circular Arc Colouring and Bandwidth Allocation in All-Optical Ring Networks”, Proceedings of the International Workshop APPROX’98: Approximation Algorithms for Combinatorial Optimization, Klaus Jansen and Jose Rolim Eds., LNCS 1444, 147–158.
E. Kumar, E. Schwabe, “Improved Access to Optical Bandwidth in Trees”, Proceedings of SODA’97, 1997.
A. Lubotzky, R. Phillips, P. Sarnak, “Ramanujan Graphs”, Combinatorica 8, 1988, 261–278.
W. Mader, “Minimale n-fach Kantenzusammenhangende Graphen”, Math. Ann. 191, 1971, 21–28.
G.A. Margulis, “Explicit Group—Theoretic Constructions of Combinatorial Schemes and their Applications for the Construction of Expanders and Concentrators”, Problemy Peredaci Informacii, 1988.
A. D. McAulay, Optical Computer Architectures, John Wiley, 1991.
C. L. Monma and V. K. Wei. “Intersection Graphs of Paths in a Tree”, Journal of Combinatorial Theory, Series B, 1986, 141–181.
R. Ramaswami, G.H. Sasaki, “Multiwavelength Optical Networks with Limited Wavelength Conversion” Proc. of IEEE Infocom 97, 1997.
R. Ramaswami, “Multi-Wavelength Lightwave Networks for Computer Communication”, IEEE Comm. Magazine 31, 1993, 78–88.
R.M. Tanner, “Explicit Construction of Concentrators from Generalized n-gons”, SIAM J. Alg. Discr. Meth., 5, 1984, 287–293.
A. Tucker. “Coloring a Family of Circular Arcs”, SIAM J. Appl. Math. 29, No. 3, 1975, 493–502.
R.J. Vetter and D.H.C. Du, “Distributed Computing with High-Speed Optical Networks”, IEEE Computer 26, 1993, 8–18.
G. Wilfong, P. Winkler, “Ring Routing and Wavelength Translation”, Proceedings of SODA’98, 1998.
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Gargano, L., Vaccaro, U. (2000). Routing in All-Optical Networks: Algorithmic and Graph-Theoretic Problems. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_45
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DOI: https://doi.org/10.1007/978-1-4757-6048-4_45
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