  We address a sequential decision problem that arises in the computation of
symmetric Boolean functions of distributed data. We consider a collocated
network, where each node's transmissions can be heard by every other node. Each
node has a Boolean measurement and we wish to compute a given Boolean function
of these measurements. We suppose that the measurements are independent and
Bernoulli distributed. Thus, the problem of optimal computation becomes the
problem of optimally ordering node's transmissions so as to minimize the total
expected number of bits. We solve the ordering problem for the class of Boolean
threshold functions. The optimal ordering is dynamic, i.e., it could
potentially depend on the values of previously transmitted bits. Further, it
depends only on the ordering of the marginal probabilites, but not on their
exact values. This provides an elegant structure for the optimal strategy. For
the case where each node has a block of measurements, the problem is
significantly harder, and we conjecture the optimal strategy.
