A polynomial-time algorithm for computing disjoint lightpath pairs in minimum isolated-failure-immune WDM optical networks

A fundamental problem in survivable routing in wavelength division multiplexing (WDM) optical networks is the computation of a pair of link-disjoint (or node-disjoint) lightpaths connecting a source with a destination, subject to the wavelength continuity constraint. However, this problem is NP-hard when the underlying network topology is a general mesh network. As a result, heuristic algorithms and integer linear programming (ILP) formulations for solving this problem have been proposed. In this paper, we advocate the use of 2-edge connected (or 2-node connected) subgraphs of minimum isolated failure immune networks as the underlying topology for WDM optical networks. We present a polynomial-time algorithm for computing a pair of link-disjoint lightpaths with shortest total length in such networks. The running time of our algorithm is O(nW2), where n is the number of nodes, and W is the number of wavelengths per link. Numerical results are presented to demonstrate the effectiveness and scalability of our algorithm. Extension of our algorithm to the node-disjoint case is straightforward.