  The speed of an exhaustive search can be measured by a cover time, which is
defined as the time it takes a random searcher to visit every state in some
target set. Cover times have been studied in both the physics and probability
literatures, with most prior works focusing on a single searcher. In this
paper, we prove an explicit formula for all the moments of the cover time for
many searchers on an arbitrary discrete network. Our results show that such
cover times depend only on properties of the network along the shortest paths
to the most distant parts of the target. This mere local dependence contrasts
with the well-known result that cover times for single searchers depend on
global properties of the network. We illustrate our rigorous results by
stochastic simulations.
