Constructing min-cost single failure immune recovery trees: Computational complexity and approximation algorithms

In this paper, we study the problem of constructing min-cost single-link/node failure immune recovery trees for two-edge/vertex connected networks. We prove its NP-hardness, and present a general framework of efficient approximation algorithms for solving this problem. Based on this framework, we present two realizations: 1) for link failure protection, our realization has an approximation ratio of 2 and O(nlog n(m +nlogn)) running time if different links have different costs, or an approximation ratio of 1.5 and a linear running time if all links have the same cost; 2) for node failure protection, our realization has an approximation ratio of 2 and O(n³m) running time if different links have different costs, or an approximation ratio of 5/3 and a linear running time if all links have the same cost.