Models, Complexity and Algorithms for the Design of Multi-fiber WDM Networks

In this paper, we study multi-fiber optical networks with wavelength division multiplexing (WDM). We extend the definition of the well-known Wavelength Assignment Problem (WAP) to the case of k fibers per link and w wavelengths per fiber, generalization that we will call (k,w)-WAP. We develop a new model for the (k,w)-WAP based on conflict hypergraphs. Furthermore, we consider two natural optimization problems that arise from the (k,w)-WAP: minimizing the number of fibers k given a number of wavelengths w, on one hand, and minimizing w given k, on the other. We develop and analyze the practical performance of two methodologies based on hypergraph coloring.