  An overarching issue in resource management of wireless networks is assessing
their capacity: How much communication can be achieved in a network, utilizing
all the tools available: power control, scheduling, routing, channel assignment
and rate adjustment? We propose the first framework for approximation
algorithms in the physical model of wireless interference that addresses these
questions in full. The approximations obtained are at most doubly logarithmic
in the link length and rate diversity. Where previous bounds are known, this
gives an exponential improvement (or better).
  A key contribution is showing that the complex interference relationship of
the physical model can be simplified, at a small cost, into a novel type of
amenable conflict graphs. We also show that the approximation obtained is
provably the best possible for any conflict graph formulation.
