  One of the most fundamental tasks in sensor networks is the computation of a
(compressible) aggregation function of the input measurements. What rate of
computation can be maintained, by properly choosing the aggregation tree, the
TDMA schedule of the tree edges, and the transmission powers? This can be
viewed as the convergecast capacity of a wireless network. We show here that
the optimal rate is effectively a constant. This holds even in \emph{arbitrary}
networks, under the physical model of interference. This compares with previous
bounds that are logarithmic (e.g., $\Omega(1/\log n)$). Namely, we show that a
rate of $\Omega(1/\log^* \Delta)$ is possible, where $\Delta$ is the length
diversity (ratio between the furthest to the shortest distance between nodes).
It also implies that the \emph{scheduling complexity} of wireless connectivity
is $O(\log^* \Delta)$. This is achieved using the natural minimum spanning tree
(MST). Our method crucially depends on choosing the appropriate power
assignment for the instance at hand, since without power control, only a
trivial linear rate can be guaranteed. We also show that there is a fixed power
assignment that allows for a rate of $\Omega(1/\log\log \Delta)$. Surprisingly,
these bounds are best possible. No aggregation network can guarantee a rate
better than $O(1/\log\log \Delta)$ using fixed power assignment. Also, when
using arbitrary power control, there are instances whose MSTs cannot be
scheduled in fewer than $\Omega(1/\log^* \Delta)$ slots.
