A fundamental problem in wireless networks is the maximum link scheduling problem: given a set $L$ of links, compute the largest possible subset $L'\subseteq L$ of links that can be scheduled simultaneously without interference. This problem is particularly challenging in the physical interference model based on SINR constraints (referred to as the SINR model), which has gained a lot of interest in recent years. Constant factor approximation algorithms have been developed for this problem, but low complexity distributed algorithms that give the same approximation guarantee in the SINR model are not known. Distributed algorithms are especially challenging in this model, because of its non-locality. In this paper, we develop a set of fast distributed algorithms in the SINR model, providing constant approximation for the maximum link scheduling problem under uniform power assignment. We find that different aspects of available technology, such as full/half-duplex communication, and non-adaptive/adaptive power control, have a significant impact on the performance of the algorithm; these issues have not been explored in the context of distributed algorithms in the SINR model before. Our algorithms' running time is $O(g(L) \log^c m)$, where $c=1,2,3$ for different problem instances, and $g(L)$ is the "link diversity" determined by the logarithmic scale of a communication link length. Since $g(L)$ is small and remains in a constant range in most cases, our algorithms serve as the first set of "sublinear" time distributed solution. The algorithms are randomized and crucially use physical carrier sensing in distributed communication steps.