Toggling dual label: an exact algorithm for finding the optimal pair of link-disjoint paths in $$\alpha +1$$ α + 1 path protection

Most network real-time applications require reliable transmission against incidents such as link failure. Path protection utilizes a link-disjoint secondary path to protect the primary path. Nevertheless, existing path protection schemes have drawbacks in either resource utilization or recovery response from link failure for real-time services. Recently, the $$\alpha +1$$ α + 1 protection was proposed to provide partial bandwidth protection for mission critical data only. The $$\alpha +1$$ α + 1 protection enables fast recovery from link failure with efficient resource utilization. However, finding the optimal pair of primary-secondary paths for $$\alpha +1$$ α + 1 protection remains a challenge. Existing paths-finding algorithms for the $$\alpha +1$$ α + 1 protection utilize the $$K$$ K -shortest path approach, considerably increasing the algorithm’s complexity. This paper presents a novel exact $$\alpha +1$$ α + 1 path-finding algorithm, called the Toggling Dual Label algorithm, to efficiently identify the optimum solution in polynomial time without utilizing the $$K$$ K -shortest path algorithm. The proposed algorithm is shown to produce the optimum solution while maintaining a low complexity.