  We seek to develop network algorithms for function computation in sensor
networks. Specifically, we want dynamic joint aggregation, routing, and
scheduling algorithms that have analytically provable performance benefits due
to in-network computation as compared to simple data forwarding. To this end,
we define a class of functions, the Fully-Multiplexible functions, which
includes several functions such as parity, MAX, and k th -order statistics. For
such functions we exactly characterize the maximum achievable refresh rate of
the network in terms of an underlying graph primitive, the min-mincut. In
acyclic wireline networks, we show that the maximum refresh rate is achievable
by a simple algorithm that is dynamic, distributed, and only dependent on local
information. In the case of wireless networks, we provide a MaxWeight-like
algorithm with dynamic flow splitting, which is shown to be throughput-optimal.
