Maximum Profit Wavelength Assignment in WDM Rings

Wavelength Division Multiplexing (WDM) is a dominating technology in contemporary all-optical networking. It allows several connections to be established through the same fiber links, provided that each of the connections uses a different wavelength. A second requirement is that a connection must use the same wavelength from one end to the other in order to avoid the use of wavelength converters which are costly or slow. In practice, the available bandwidth is limited to few dozens, or at most hundreds, wavelengths per fiber and the situation is not expected to change in the near future. It is therefore impossible to serve a large set of communication requests simultaneously. It thus makes sense to consider the problem of satisfying a maximum profit subset of requests, where profits may represent priorities or actual revenues related to requests. In our model, requests are undirected, which corresponds to full-duplex communication. We describe a request by its connection path and its profit, and formulate the problem in graph-theoretic terms as follows: