  Advances in optimization and constraint satisfaction techniques, together
with the availability of elastic computing resources, have spurred interest in
large-scale network verification and synthesis. Motivated by this, we consider
the top-down synthesis of ad-hoc IoT networks for disaster response and search
and rescue operations. This synthesis problem must satisfy complex and
competing constraints: sensor coverage, line-of-sight visibility, and network
connectivity. The central challenge in our synthesis problem is quickly scaling
to large regions while producing cost-effective solutions. We explore two
qualitatively different representations of the synthesis problems
satisfiability modulo convex optimization (SMC), and mixed-integer linear
programming (MILP). The former is more expressive, for our problem, than the
latter, but is less well-suited for solving optimization problems like ours. We
show how to express our network synthesis in these frameworks, and, to scale to
problem sizes beyond what these frameworks are capable of, develop a
hierarchical synthesis technique that independently synthesizes networks in
sub-regions of the deployment area, then combines these. We find that, while
MILP outperforms SMC in some settings for smaller problem sizes, the fact that
SMC's expressivity matches our problem ensures that it uniformly generates
better quality solutions at larger problem sizes.
