Resolution of a Routing and Wavelength Assignment Problem by Independent Sets in Conflict Graphs

In an optical network, a Scheduled Lightpath Demand (SLD) is a connection demand between two nodes, during a certain time and with a certain wavelength. We consider the following NP-hard Routing and Wavelength Assignment problem dealing with SLDs: given a set of SLDs and a number W of wavelengths, maximize the number of SLDs to which we can assign a lightpath (i.e. a routing path and a wavelength) without exceeding the number W of available wavelengths. The constraints are: a same wavelength must be assigned all along the routing path of any SLD; at any time, a given wavelength on a given edge of the network cannot be used to satisfy more than one SLD. To solve this problem, we study an approach stating the problem as the successive searches of independent sets in some conflict graphs. Moreover, we improve this approach thanks to a post-optimization method. The experimental results show that this model and the post-optimization method are quite efficient to provide a large number of routed SLDs.