Routing and wavelength assignment in multifiber WDM networks with non-uniform fiber cost

Motivated by the increasing importance of multifiber WDM networks we study a routing and wavelength assignment problem in such networks. In this problem the number of wavelengths per fiber is given and the goal is to minimize the cost of fiber links that need to be reserved in order to satisfy a set of communication requests; we introduce a generalized setting where network pricing is non-uniform, that is the cost of hiring a fiber may differ from link to link. We consider two variations: undirected, which corresponds to full-duplex communication, and directed, which corresponds to one-way communication. Moreover, for rings we also study the problem in the case of pre-determined routing. We present exact or constant-ratio approximation algorithms for all the above variations in chain, ring and spider networks.