  We consider the problem of far-field sensing by means of a sensor array.
Traditional array geometry design techniques are agnostic to prior information
about the far-field scene. However, in many applications such priors are
available and may be utilized to design more efficient array topologies. We
formulate the problem of array geometry design with scene prior as one of
finding a sampling configuration that enables efficient inference, which turns
out to be a combinatorial optimization problem. While generic combinatorial
optimization problems are NP-hard and resist efficient solvers, we show how for
array design problems the theory of submodular optimization may be utilized to
obtain efficient algorithms that are guaranteed to achieve solutions within a
constant approximation factor from the optimum. We leverage the connection
between array design problems and submodular optimization and port several
results of interest. We demonstrate efficient methods for designing arrays with
constraints on the sensing aperture, as well as arrays respecting combinatorial
placement constraints. This novel connection between array design and
submodularity suggests the possibility for utilizing other insights and
techniques from the growing body of literature on submodular optimization in
the field of array design.
