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An important feature of MPLS networks is local restoration where detour paths are set-up a priori. The detour is such that failed links or nodes can be bypassed locally from the first node that is upstream from the failures. This local bypass activation from the first detection point for failures permits much faster recovery than end-to-end path based mechanisms that require failure information to propagate to the network edges. However, local restoration of bandwidth guaranteed connections can be expensive in the additional network capacity needed. Hence, it is important to minimize and share restoration capacity. The problem of routing with local restoration requirements has been studied previously in a dynamic on-line setting. However, there are no satisfactory algorithms for the problem of pre-provisioning fast restorable connections when the aggregate traffic demands are known (as would be the case when a set of routers are to be interconnected over an optical network or for pre-provisioned ATM over MPLS overlays). The contribution of this paper is a fast combinatorial approximation algorithm for maximizing throughput when the routed traffic is required to be locally restorable. To the best of our knowledge, this is the first combinatorial algorithm for the problem with a performance guarantee. Our algorithm is a fully polynomial time approximation scheme (FPTAS), i.e., for any given ε>0, it guarantees (1+ε)-factor closeness to the optimal solution, and runs in time polynomial in the network size and 1/ε. We compare the throughput of locally restorable routing with that of unprotected routing and 1+1-dedicated path protection on representative ISP topologies.