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Given a set of demands between pairs of nodes, we examine the traffic engineering problem of flow routing and fair bandwidth allocation where flows can be split to multiple paths (e.g., MPLS tunnels). This paper presents an algorithm for finding an optimal and global per-commodity max-min fair rate vector in a polynomial number of steps. In addition, we present a fast and novel distributed algorithm where each source router can find the routing and the fair rate allocation for its commodities while keeping the locally optimal max-min fair allocation criteria. The distributed algorithm is a fully polynomial epsilon-approximation (FPTAS) algorithm and is based on a primal-dual alternation technique. We implemented these algorithms to demonstrate its correctness, efficiency, and accuracy.