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A distributed scheduling algorithm is proposed for achieving end-to-end flow max-min fairness in wireless multi-hop networks. The problem is modeled as an optimization problem by taking into account the MAC-layer constraints. With dual programming and Lagrange relaxation, the problem is decomposed into two subproblems, one is for transport layer at the source node, and the other for MAC layer in the network. A max-price based max-min fair rate allocation algorithm is adopted for the transport layer subproblem and an algorithm based on integer programming is designed for scheduling link activities at MAC layer. Simulation results show that the proposed algorithm can achieve conflict-free schedule for wireless links and provide max-min fairness for end-to-end flows efficiently.