Approximate algorithms for survivable network design

Along with the rapid development of network communication technology and the explosive growth of the internet applications, network reliability appears increasingly important to both traditional areas such as defense, finance and power industry, and emerging areas such as trusted computing, cloud computing and next-generation Internet. An interesting subject that has attracted great effort is how to design network topologies with a minimum network resource usage in terms of cost that provides a relibility guarantee. As problems on this subject, like most other network optimization problems, are well-known NP-hard even in their simplest form, design of effective solutions with a guaranteed approximation ratio from the optimal solution has been a major research focus of great significance for both theory and applications. This survery summarizes major existing techniques and results for solving some central problems in designing survivable networks including the minimal connected subgraph problem, the survivable network design problem and the Steiner minimal network problem.