Abstract
We introduce a problem directly inspired by its application to DWDM (dense wavelength division multiplexing) network design. We are given a set of demands to be carried over a network. Our goal is to choose a route for each demand and to decompose the network into a collection of edge-disjoint simple paths. These paths are called optical line systems. The cost of routing one unit of demand is the number of line systems with which the demand route overlaps; our design objective is to minimize the total cost over all demands. This cost metric is motivated by the need to avoid O-E-O (optical-electrical-optical) conversions in optical transmission as well as to minimize the expense of the equipment necessary to carry the traffic.
For given line systems, it is easy to find the optimal demand routes. On the other hand, for given demand routes designing the optimal line systems can be NP-hard. We first present a 2-approximation for general network topologies. As optical networks often have low node degrees, we also offer an algorithm that finds the optimal solution for the special case in which the node degree is at most 3.
If neither demand routes nor line systems are fixed, the situation becomes much harder. Even for a restricted scenario on a 3-regular Hamiltonian network, no efficient algorithm can guarantee a constant approximation better than 2. For general topologies, we offer a simple algorithm with an O(log K)- and an O(log n)-approximation where K is the number of demands and n is the number of nodes. For rings, a common special topology, we offer a 3/2-approximation.
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
Anshelevich, E., Zhang, L.: Path Decomposition under a New Cost Measure with Applications to Optical Network Design (full version), http://www.cs.cornell.edu/people/eanshel/
Bazgan, C., Santha, M., Tuza, Z.: On the approximability of finding a(nother) Hamiltonian cycle in cubic Hamiltonian graphs. Journal of Algorithms 31, 249–268
Bermond, J.-C., Marlin, N., Peleg, D., Pérennes, S.: Virtual path layouts with low congestion or low diameter in ATM networks. In: Proceedings of lère Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (1999)
Cosares, S., Saniee, I.: An optimization problem related to balancing loads on SONET rings. Telecommunications Systems 3, 165–181 (1994)
Doshi, B., Nagarajan, R., Blackwood, N., Jothipragasam, S., Raman, N., Sharma, M., Prasanna, S.: LIPI: A lightpath intelligent instantiation tool: capabilities and impact. Bell Labs Technical Journal (2002)
Fishburn, P.: Interval orders and interval graphs. Wiley and Sons, New York (1985)
Fortune, S., Sweldens, W., Zhang, L.: Line system design for DWDM networks (submitted)
Garey, M.R., Johnson, D.S.: Computers and intractability - A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)
Gerstel, O., Segall, A.: Dynamic maintenance of the virtual path layout. In: Proceedings of IEEE INFOCOM 1995 (April 1995)
Khanna, S.: A polynomial-time approximation scheme for the SONET ring loading problem. Bell Labs Technical Journal (1997)
Kleinberg, J., Kumar, A.: Wavelength conversion in optical networks. In: SODA 1999, pp. 566–575 (1999)
Kumar, V., Schwabe, E.: Improved access to optical bandwidth in trees. In: SODA 1997, pp. 437–444 (1997)
Lee, W.: Personal communication (2003)
Matoušek, J.: On embedding trees into uniformly convex banach spaces. Israel Journal of Mathematics 114, 221–237 (1999)
Mihail, M., Kaklamanis, C., Rao, S.: Efficient access to optical bandwidth. In: FOCS 1995, pp. 548–557 (1995)
Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization. Dover Publications, Mineola (1998)
Raghavan, P., Upfal, E.: Efficient routing in all-optical networks. In: STOC 1994, pp. 134–143 (1994)
Ramaswami, R., Sivarajan, K.: Optical networks A practical perspective. Morgan Kaufmann, San Francisco (1998)
Schrijver, A., Seymour, P.D., Winkler, P.: The ring loading problem. SIAM Journal of Discrete Math 11(1), 1–14 (1998)
Wilfong, G., Winkler, P.: Ring routing and wavelength translation. In: SODA 1998, pp. 333–341 (1998)
Winkler, P., Zhang, L.: Wavelength assignment and generalized interval graph coloring. In: SODA 2003 (2003)
Zaks, S.: Path Layout in ATM Networks - A Survey. In: Mavronicolas, M., Merritt, M., Shavit, N. (eds.) Networks in Distributed Computing. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, pp. 145–160 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anshelevich, E., Zhang, L. (2004). Path Decomposition Under a New Cost Measure with Applications to Optical Network Design. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-30140-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23025-0
Online ISBN: 978-3-540-30140-0
eBook Packages: Springer Book Archive