A new survivable mapping problem in IP-over-WDM networks

We introduce a new version of the widely studied survivable mapping problem in IP-over-WDM networks. Unlike the original survivable mapping problem, the new survivable mapping problem (NSM) allows the given logical topology to be augmented by adding new logical links to it. NSM is stated as follows: given a physical topology and a logical topology, compute a survivable logical topology that contains the given logical topology such that the minimal survivable mapping cost for the resulting logical topology is minimized. The problem is significant for two reasons. First, if the given logical topology does not have a survivable mapping, we can add logical links to it to enable a survivable mapping. Second, if the given logical topology has a survivable mapping, it is possible to reduce the minimal survivable mapping cost by adding logical links to the given logical topology. We first prove that a solution to NSM always exists and then provide a straightforward integer linear program (ILP) formulation for NSM. Moreover, we present a theoretical result that leads to an improved ILP formulation for NSM and an NP-hardness proof for NSM. The significance of both the new survivable mapping problem and the theoretical result is demonstrated by simulation