Survivable Mapping of Virtual Topologies for Double-Node Failure

In multilayer network design, the mapping of logical links onto the physical layer plays a critical role in failure tolerance of the network. Since a single link or node failure in the physical layer can bring several logical links down, it is important to find a mapping of logical links on the physical layer that ensures the logical topology remains connected in case of physical failures. A mapping that preserves the logical-layer connectivity in case of any given failure of the physical layer is called survivable. The problem of finding a survivable mapping for single-link failure for a given logical network over a given physical network is known to be NP-complete. We show that it is also true for both single- and double-node failure. Thus, for practical applications, only scalable heuristic methods can be used. In the literature, efficient and scalable combinatorial mapping algorithms were proposed for single- or multiple-link failures and single-node failures of the physical network, which are based on specific properties of the network graphs. As a new result, in this paper we present a graph-theoretic heuristic method to find a survivable mapping for double-node failures. We also present an integer linear programming (ILP) model and evaluate the efficiency of the algorithm by comparing it to the ILP method.