  How should we gather information in a network, where each node's visibility
is limited to its local neighborhood? This problem arises in numerous
real-world applications, such as surveying and task routing in social networks,
team formation in collaborative networks and experimental design with
dependency constraints. Often the informativeness of a set of nodes can be
quantified via a submodular utility function. Existing approaches for
submodular optimization, however, require that the set of all nodes that can be
selected is known ahead of time, which is often unrealistic. In contrast, we
propose a novel model where we start our exploration from an initial node, and
new nodes become visible and available for selection only once one of their
neighbors has been chosen. We then present a general algorithm NetExp for this
problem, and provide theoretical bounds on its performance dependent on
structural properties of the underlying network. We evaluate our methodology on
various simulated problem instances as well as on data collected from social
question answering system deployed within a large enterprise.
