On Scheduling Problems with Applications to Packet-Switched 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-hard for both the preemptive and the non-preemptive cases. Furthermore, we propose two eÆcient approximation algorithms. The rst is for the preemptive case and it is based on a natural decomposition of the problem to the classical multiprocessor scheduling and open-shop problems. For the non-preemptive 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 re ned version of list scheduling and we prove it to be a 2-approximation algorithm for both the o -line and the on-line contexts.