Abstract
Motivated by the problem of efficient routing in all-optical networks, we study a constrained version of the bipartite edge coloring problem. We show that if the edges adjacent to a pair of opposite vertices of an L-regular bipartite graph are already colored with αL different colors, then the rest of the edges can be colored using at most (1+α/2)L colors. We also show that this bound is tight by constructing instances in which (1+α/2)L colors are indeed necessary. We also obtain tight bounds on the number of colors that each pair of opposite vertices can see.
Using the above results, we obtain a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed fiber link on a directed fiber tree using at most 5/3L wavelengths. This improves previous results of [9, 7, 6, 10]. We also obtain that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus that our algorithm is optimal in the class of greedy algorithms which includes the algorithms presented in [9, 7, 6, 10].
Partially supported by Progetto MURST 40%, Algoritmi, Modelli di Calcolo e Strutture Informative and by EU Esprit Project GEPPCOM and ALCOM-IT.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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.
B. Beauquier, J.-C. Bermond, L. Gargano, P. Hell, S. Perennes, U. Vaccaro, Graph Problems arising from Wavelength-Routing in All-Optical Networks, in proc. of Workshop on Optics in Computer Science, 1997.
C. Berge, Graphs, North-Holland.
J.-C. Bermond, L. Gargano, S. Perennes, A. A. Rescigno, and U. Vaccaro, Efficient Collective Communication in Optical Networks, in Proc. of ICALP 96.
P. E. Green, Fiber Optic Communication Networks, Prentice Hall, 1992.
C. Kaklamanis and P. Persiano, Efficient Wavelength Routing on Directed Fiber Trees, in Proc. of Algorithms-ESA '96, Lecture Notes in Computer Science, 1136, pp. 460–470.
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.
V. Kumar and E. J. Schwabe. Improved access to optical bandwidth in trees. In Proceedings of SODA '97, 1997.
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.
R. Pankaj, Architectures for Linear Lightwave Networks, Ph.D. Thesis, MIT, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaklamanis, C., Persiano, P., Erlebach, T., Jansen, K. (1997). Constrained bipartite edge coloring with applications to wavelength routing. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_205
Download citation
DOI: https://doi.org/10.1007/3-540-63165-8_205
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63165-1
Online ISBN: 978-3-540-69194-5
eBook Packages: Springer Book Archive