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We study efficient interference-aware joint routing and TDMA link scheduling for a multihop wireless network to maximize its throughput. Efficient link scheduling can greatly reduce the interference effect of close-by transmissions. Unlike the previous studies that often assume a unit disk graph model, we assume that different terminals could have different transmission ranges and interference ranges. In our model, a communication link may not exist due to barriers or is not used by a predetermined routing protocol. Using a mathematical formulation, we develop interference aware joint routing and TDMA link schedulings that optimize the networking throughput subject to various constraints. Our linear programming formulation will find a flow routing whose achieved throughput (or fairness) is at least a constant fraction of the optimum. Then, by assuming known link capacities and link traffic loads, we study link scheduling under the RTS/CTS interference model and the protocol interference model with fixed transmission power. For both models, we present both efficient centralized and distributed algorithms that use time slots within a constant factor of the optimum. We also present efficient distributed algorithms whose performances are still comparable with optimum, but with much less communications. Our theoretical results are corroborated by extensive simulation studies.