  Recently, it has been shown that CSMA algorithms which use queue length-based
link weights can achieve throughput optimality in wireless networks. In
particular, a key result by Rajagopalan, Shah, and Shin (2009) shows that, if
the link weights are chosen to be of the form log(log(q)) (where q is the
queue-length), then throughput optimality is achieved. In this paper, we
tighten their result by showing that throughput optimality is preserved even
with weight functions of the form log(q)/g(q), where g(q) can be a function
that increases arbitrarily slowly. The significance of the result is due to the
fact that weight functions of the form log(q)/g(q) seem to achieve the best
delay performance in practice.
