  The capacity of a wireless network is the maximum possible amount of
simultaneous communication, taking interference into account.
  Formally, we treat the following problem. Given is a set of links, each a
sender-receiver pair located in a metric space, and an assignment of power to
the senders. We seek a maximum subset of links that are feasible in the SINR
model: namely, the signal received on each link should be larger than the sum
of the interferences from the other links. We give a constant-factor
approximation that holds for any length-monotone, sub-linear power assignment
and any distance metric.
  We use this to give essentially tight characterizations of capacity
maximization under power control using oblivious power assignments.
Specifically, we show that the mean power assignment is optimal for capacity
maximization of bi-directional links, and give a tight $\theta(\log
n)$-approximation of scheduling bi-directional links with power control using
oblivious power. For uni-directional links we give a nearly optimal $O(\log n +
\log \log \Delta)$-approximation to the power control problem using mean power,
where $\Delta$ is the ratio of longest and shortest links. Combined, these
results clarify significantly the centralized complexity of wireless
communication problems.
