Models, complexity and algorithms for the design of multifiber WDM networks

We study multifiber optical networks with wavelength division multiplexing (WDM). Assuming that the lightpaths use the same wavelength from source to destination, we extend the definition of the well-known wavelength assignment problem (WAP), to the case where there are k fibers per link, and w wavelengths per fiber are available: This generalization is called the (k, ω)-WAP. We develop a new model for the (k, ω)-WAP, based on conflict hypergraphs: conflict hypergraphs more accurately capture the lightpath interdependencies, generalizing the conflict graphs used for single-fiber networks. By relating the (k, ω)-WAP with the hypergraph coloring problem, we prove that the former is NP-complete, and present further results with respect to the complexity of that problem. We consider the two natural optimization problems that arise from the (k, w)-WAP: the problem of minimizing k given w, and that of minimizing w given k. We develop and analyze the practical performances of two methodologies based on hypergraph coloring, one for each of the two optimization problems, on existing backbone networks in Europe and in the USA. The first methodology relies on two heuristics based on a randomized approximation algorithm and the second consists on an integer programming formulation.