In high-performance computing, there is great opportunity for systems
that use FPGAs to handle communication while also performing
computation on data in transit in an ``altruistic'' manner--that is,
using resources for computation that might otherwise be used for
communication, and in a way that improves overall system performance
and efficiency. We provide a specific definition of \textbf{Computing
in the Network} that captures this opportunity. We then outline some
overall requirements and guidelines for cooperative computing that
include this ability, and make suggestions for specific computing
capabilities to be added to the networking hardware in a system. We
then explore some algorithms running on a network so equipped
for a few specific computing tasks: dense matrix multiplication,
sparse matrix transposition and sparse matrix multiplication. In the
first instance we give limits of problem size and estimates of
performance that should be attainable with present-day FPGA hardware
