  We consider the capacity problem (or, the single slot scheduling problem) in
wireless networks. Our goal is to maximize the number of successful connections
in arbitrary wireless networks where a transmission is successful only if the
signal-to-interference-plus-noise ratio at the receiver is greater than some
threshold. We study a game theoretic approach towards capacity maximization
introduced by Andrews and Dinitz (INFOCOM 2009) and Dinitz (INFOCOM 2010). We
prove vastly improved bounds for the game theoretic algorithm. In doing so, we
achieve the first distributed constant factor approximation algorithm for
capacity maximization for the uniform power assignment. When compared to the
optimum where links may use an arbitrary power assignment, we prove a $O(\log
\Delta)$ approximation, where $\Delta$ is the ratio between the largest and the
smallest link in the network. This is an exponential improvement of the
approximation factor compared to existing results for distributed algorithms.
All our results work for links located in any metric space. In addition, we
provide simulation studies clarifying the picture on distributed algorithms for
capacity maximization.
