Abstract
We study the problem of routing and scheduling requests of limited durations in an all-optical network. The task is servicing the requests, assigning each of them a route from source to destination, a starting time and a wavelength, with restrictions on the number of available wavelengths. The goal is minimizing the overall time needed to serve all requests. We study the relationship between this problem and minimum path coloring and we show how to exploit known results on path coloring to derive approximation scheduling algorithms for meshes, trees and nearly-Eulerian, uniformly high-diameter graphs. Independently from the relationship with path coloring we propose different approximation algorithms for call scheduling in trees and in trees of rings. As a side result, we present a constant approximation algorithm for star networks. We assume for simplicity that all calls are released at time 0, however all our results hold also for arbitrary release dates at the expense of a factor 2 in the approximation ratio.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Aumann and Y. Rabani. Improved bounds for all-optical routing. In Proc. of the 6-th ACM Symposium on Discrete Algorithms, pages 567–576, 1995.
Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical-routing. In Proc. of the 28th Annual Symposium on the Theory of Computing, pages 531–540, 1996.
Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloquium on Automata, Languages and Programming, volume 1256 of Lectures Notes in Computer Science, pages 516–526, 1997.
L. Becchetti, M. Di Ianni, and A. Marchetti-Spaccamela. Approximation Algorithms for Routing and Call Scheduling in all-optical Chains and Rings. In Proc. of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science, volume 1738 of Lectures Notes in Computer Science, pages 201–212, 1999.
C. Brackett. Dense Wavelength Division Multiplexing Networks: Principles and Applications. IEEE Journal Selected Areas in Comm., 8:948–964, 1990.
J. Van Leeuwen editor. Handbook of Theoretical Computer Science. Volume A: Algorithms and Complexity. Elesevier North-Holland, Amsterdam, 1990.
T. Erlebach and K. Jansen. Scheduling Virtual Connections in Fast Networks. In Proc. of the 4th Parallel Systems and Algorithms Workshop PASA’ 96, 1996.
T. Erlebach and K. Jansen. Call Scheduling in Trees, Rings and Meshes. In Proc. of the 30th Hawaii International Conference on System Sciences, 1997.
T. Erlebach and K. Jansen. Off-line and on-line call-scheduling in stars and trees. In WG: Graph-Theoretic Concepts in Computer Science, International Workshop WG, volume 1335 of Lecture Notes in Computer Science, 1997.
T. Erlebach, K. Jansen, C. Kaklamanis, M. Mihail, and P. Persiano. Optimal Wavelength Routing on Directed Fiber Tree. Theoretical Computer Science, 221(1-2):119–137, 1999.
P. E. Green. Fiber-optic Communication Networks. Prentice-Hall, 1992.
M. Di Ianni. Efficient delay routing. Theoretical Computer Science, 196:131–151, 1998.
S. Khanna. A Polynomial Time Approximation Scheme for the SONET Ring Loading Problem. Bell Labs Tech. J., Spring, 1997.
J. Kleinberg and E. Tardos. Approximations for the disjoint paths problem in high-diameter planar networks. In Proc. of 27th ACM Symposium on the Theory Of Computing, pages 26–35, 1995.
F.T. Leighton, B.M. Maggs, and A.W. Richa. Fast Algorithms for Finding O(Congestion+Dilation) Packet Routing Schedules. In Proc. of 28th Annual Hawaii International Conference on System Sciences, pages 555–563, 1995.
T. Leighton, B. Maggs, and S. Rao. Packet routing and jobshop scheduling in O(congestion+dilation) steps. Combinatorica, 14, 1994.
K. Nosu N. K. Cheung and G. Winzer. Dense Wavelength Division Multiplexing Networks: Principles and Applications. IEEE Journal Selected Areas in Comm., 8, 1990.
Y. Rabani. Path coloring on the mesh. In Proc. of 37th Annual IEEE Symposium Foundations of Computer Science, pages 400–409, 1996.
P. Raghavan and E. Upfal. Efficient Routing in All-Optical Networks. In Proc. of the 26th Annual Symposium on the Theory of Computing, pages 134–143, 1994.
D. B. Shmoys, J. Wein, and D. P. Williamson. Scheduling parallel machines on-line. SIAM Journal of Computing, 24 (6):1313–1331, 1995.
B. Zelinka. Medians and Peripherians on Trees. Arch. Math. (Brno), pages 87–95, 1969.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becchetti, L., Di Ianni, M., Marchetti-Spaccamela, A. (2000). Approximating Call-Scheduling Makespan in All-Optical Networks. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-40064-8_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41183-3
Online ISBN: 978-3-540-40064-6
eBook Packages: Springer Book Archive