Minimum cost ring survivability in WDM networks

Recently, E. Modiano and A. Narula-Tam (see Proc. IEEE INFOCOM´01, 2001) introduced the notion of survivable routing and established a necessary and sufficient condition for the existence of survivable routes for a given logical topology in a physical topology. In two earlier papers, we showed that the survivability problem is NP-complete, both when the nodes of the logical topology are unlabeled (Sen, A. et al., Proc. IEEE Int. Commun. Conf. ICC´02, 2002) or labeled (Sen et al., Proc. IEEE Int. Symp. on Computers and Commun. ISCC´02, 2002). We also gave algorithms to test if survivable routing of a logical ring is possible in a WDM network with arbitrary physical topology. We now address finding the minimum number of links that have to be added to a physical topology so that the survivable routing of a logical ring is possible. We show that, not only is this problem NP-complete, but an ε-approximation algorithm for the problem cannot be found unless P=NP. We provide an ILP formulation for finding the optimal solution of the problem. We also provide an approximate solution of the problem. The approximate algorithm requires only a very small fraction of the time required by the optimal algorithm, but produces results that are close to the optimal solution on two test networks - ARPANET and the Italian National Network.