Fast Exact ILP Decompositions for Ring RWA

• Published in: Journal of optical communications and networking Vol. 3; no. 7; pp. 577 - 586
• Main Authors: Yetginer, E., Liu, Z., Rouskas, G. N.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.07.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clocks; Color; Computer networks; Decomposition; Integer linear programming (ILP); Management information systems; Mathematical analysis; Mathematical models; Networks; Optimized production technology; Partitioning; Ring networks; Routing; Routing and wavelength assignment (RWA); SONET; Studies; Wavelength assignment; Wavelength division multiplexing; Wavelengths
• ISSN: 1943-0620; 1943-0639
• DOI: 10.1364/JOCN.3.000577

Wavelength division multiplexing rings are now capable of supporting more than 100 wavelengths over a single fiber. Conventional link and path formulations for the routing and wavelength assignment problem are inefficient due to the inherent symmetry in wavelength assignment and the fact that the problem size increases fast with the number of wavelengths. Although a formulation based on maximal independent sets (MIS) does not have these drawbacks, it suffers from exponential growth in the number of variables with increasing network size. We develop a new ILP (integer linear program) formulation based on the key idea of partitioning the path set and representing the MIS in the original network using the independent sets calculated in each of these partitions. This exact decomposition trades off the number of variables with the number of constraints and, as a result, achieves a much better scalability in terms of network dimension. Numerical results on ring networks of various sizes demonstrate that this new ILP decomposition achieves a decrease of several orders of magnitude in running time compared to existing formulations. Our main contribution is a novel and extremely fast technique for obtaining, in a few seconds using commodity CPUs, optimal solutions to instances of maximum size SONET rings with any number of wavelengths; such instances cannot be tackled with classical formulations without vast investments in computational resources and time.