Due to the wide range of services being supported, telecommunications networks are loaded with massive quantities of information. This stimulates extra concern for network survivability. In this paper, we use graph theoretic techniques for addressing network survivability issues by transforming the original network topology onto a trellis graph, which allows the application of computationally efficient methods to find disjoint routing paths. We investigate the time complexity of the new algorithm as well as the time complexity of another algorithm on trellis transformations, presented in our previous work. The two algorithms are compared and evaluated in terms of their time complexity. Conclusions on their performance are drawn which show that the new algorithm has a better performance by a factor of n, where n is the number of nodes in the network.