Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region. In contrast, in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size. First, using a combination of graph partitioning techniques and Lyapunov arguments, we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor. Then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks, and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models. Specifically, given any epsilon > 0, the maximum throughput region can be approximated in these networks within a factor of 1 - epsilon using a computation time that depends only on the maximum node degree and epsilon.