  This work concerns developing communication- and computation-efficient
methods for large-scale multiple testing over networks, which is of interest to
many practical applications. We take an asymptotic approach and propose two
methods, proportion-matching and greedy aggregation, tailored to distributed
settings. The proportion-matching method achieves the global BH performance yet
only requires a one-shot communication of the (estimated) proportion of true
null hypotheses as well as the number of p-values at each node. By focusing on
the asymptotic optimal power, we go beyond the BH procedure by providing an
explicit characterization of the asymptotic optimal solution. This leads to the
greedy aggregation method that effectively approximates the optimal rejection
regions at each node, while computation efficiency comes from the greedy-type
approach naturally. Moreover, for both methods, we provide the rate of
convergence for both the FDR and power. Extensive numerical results over a
variety of challenging settings are provided to support our theoretical
findings.
