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/spl epsiv/-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.