Network Virtualization Technology is serving as an effective method for providing a flexible and highly adaptable shared substrate network to satisfy the diversity of demands. But the problem of efficiently embedding Virtual Network (VN) onto substrate network is intractable since it is NP-hard. How to guarantee survivability of the embedding efficiently is another great challenge. In this paper, we investigate the Survivable Virtual Network Embedding (SVNE) problem and propose two efficient algorithms for solving this problem efficiently. Firstly, we formulate the model with minimum-cost objective of survivable network virtualization problem by Mixed Integer Linear Programming (MILP). We then devise two efficient relaxation-based algorithms for solving survivable virtual network embedding problem: (1) Lagrangian Relaxation based algorithm, called LR-SVNE in this paper; (2) Decomposition based algorithm called DSVNE in this paper. The results of simulation experiments show that these two algorithms both have good performance on time efficiency but LR-SVNE can guarantee the solution converge to optimal one under small scale substrate network.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.