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A fundamental problem in wireless networks is the maximum link schedulingproblem: given a set $L$ of links, compute the largest possible subset$L'\subseteq L$ of links that can be scheduled simultaneously withoutinterference. This problem is particularly challenging in the physicalinterference model based on SINR constraints (referred to as the SINR model),which has gained a lot of interest in recent years. Constant factorapproximation algorithms have been developed for this problem, but lowcomplexity distributed algorithms that give the same approximation guarantee inthe SINR model are not known. Distributed algorithms are especially challengingin this model, because of its non-locality.  In this paper, we develop a set of fast distributed algorithms in the SINRmodel, providing constant approximation for the maximum link scheduling problemunder uniform power assignment. We find that different aspects of availabletechnology, such as full/half-duplex communication, and non-adaptive/adaptivepower control, have a significant impact on the performance of the algorithm;these issues have not been explored in the context of distributed algorithms inthe 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 "linkdiversity" determined by the logarithmic scale of a communication link length.Since $g(L)$ is small and remains in a constant range in most cases, ouralgorithms serve as the first set of "sublinear" time distributed solution. Thealgorithms are randomized and crucially use physical carrier sensing indistributed communication steps.

Efficient Algorithms for Maximum Link Scheduling in Distributed Computing Models with SINR Constraints