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We address a sequential decision problem that arises in the computation ofsymmetric Boolean functions of distributed data. We consider a collocatednetwork, where each node's transmissions can be heard by every other node. Eachnode has a Boolean measurement and we wish to compute a given Boolean functionof these measurements. We suppose that the measurements are independent andBernoulli distributed. Thus, the problem of optimal computation becomes theproblem of optimally ordering node's transmissions so as to minimize the totalexpected number of bits. We solve the ordering problem for the class of Booleanthreshold functions. The optimal ordering is dynamic, i.e., it couldpotentially depend on the values of previously transmitted bits. Further, itdepends only on the ordering of the marginal probabilites, but not on theirexact values. This provides an elegant structure for the optimal strategy. Forthe case where each node has a block of measurements, the problem issignificantly harder, and we conjecture the optimal strategy.

Optimal ordering of transmissions for computing Boolean threhold functions