—Optimal scheduling for concurrent transmissions in rate-nonadaptive wireless networks is NP-hard. Optimal scheduling in rate-adaptive wireless networks is even more difficult, because, due to mutual interference, each flow’s throughput in a time slot is unknown before the scheduling decision of that slot is finalized. The capacity bound derived for ratenonadaptive networks is no longer applicable either. In this paper, we first formulate the optimal scheduling problems with and without minimum per-flow throughput constraints. Given the hardness of the problems and the fact that the scheduling decisions should be made within a few milliseconds, we propose two simple yet effective searching algorithms which can quickly move towards better scheduling decisions. Thus, the proposed scheduling algorithms can achieve high network throughput and maintain long-term fairness among competing flows with low computational complexity. For the constrained optimization problem involved, we ...