We propose a new class of distributed scheduling policies for ad hoc wireless networks that can achieve provable capacity regions. Previously known scheduling policies that guarantee comparable capacity regions are either centralized or require computation time that increases with the size of the network. In contrast, the unique feature of the proposed distributed scheduling policies is that they are constant-time policies, i.e., given a fixed approximation ratio and a hounded maximum node-degree of the network, the time needed for computing a new schedule is independent of the network size. Hence, they can be easily deployed in large networks.