The Scheduling and Wavelength Assignment Problem in Optical WDM Networks

We consider a scheduling problem, which we call the scheduling and wavelength assignment (SWA) problem, arising in optical networks that are based on the wavelength-divisionmultiplexing (WDM) technology. We prove that the SWA problem is -complete for both the preemptive and the nonpreemptive cases. Furthermore, we propose two efficient approximation algorithms. The first is for the preemptive case and is based on a natural decomposition of the problem to the classical multiprocessor scheduling and open-shop problems. For the nonpreemptive case, we prove that a naive implementation of list scheduling produces a schedule that can be times far from the optimum, where is the number of processors (equivalently, WDM channels). Finally, we give a more refined version of list scheduling and we prove it to be a 2-approximation algorithm for both the off-line and the on-line contexts.