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The design of survivable mesh based communication networks has received considerable attention in recent years. One task is to route backup paths and allocate spare capacity in the network to guarantee seamless communications services survivable to a set of failure scenarios. This is a complex multi-constraint optimization problem, called the spare capacity allocation (SCA) problem. This paper unravels the SCA problem structure using a matrix-based model, and develops a fast and efficient approximation algorithm, termed successive survivable routing (SSR). First, per-flow spare capacity sharing is captured by a spare provision matrix (SPM) method. The SPM matrix has a dimension the number of failure scenarios by the number of links. It is used by each demand to route the backup path and share spare capacity with other backup paths. Next, based on a special link metric calculated from SPM, SSR iteratively routes/updates backup paths in order to minimize the cost of total spare capacity. A backup path can be further updated as long as it is not carrying any traffic. Furthermore, the SPM method and SSR algorithm are generalized from protecting all single link failures to any arbitrary link failures such as those generated by Shared Risk Link Groups or all single node failures. Numerical results comparing several SCA algorithms show that SSR has the best trade-off between solution optimality and computation speed.