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-division-multiplexing (WDM) technology. We prove that the SWA problem is NP-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 m times far from the optimum, where m 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.