While most networks have long lifetimes, temporary network infrastructure is often useful for special events, pop-up retail, or disaster response. Aninstant IoTnetwork is one that is rapidly constructed, used for a few days, then dismantled. We consider the synthesis of instant IoT networks in urban settings. 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 quicklyscalingto large regions while producing cost-effective solutions. We explore two qualitatively different representations of the synthesis problems using 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. To scale to problem sizes beyond what these frameworks are capable of, we develop ahierarchical synthesistechnique 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.

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is specified in some discrete space, leading to difficult nonconvex optimization problems. In this paper, we connect the model selection problem with structure-promoting regularizers to submodular function minimization with continuous and discrete arguments. In particular, we leverage the theory of submodular functions to identify a class of these problems that can be solved exactly and efficiently with an agnostic combination of discrete and continuous optimization routines. We show how simple continuous or discrete constraints can also be handled for certain problem classes and extend these ideas to a robust optimization framework. We also show how some problems outside of this class can be embedded into the class, further extending the class of problems our framework can accommodate. Finally, we numerically validate our theoretical results with several proof-of-concept examples with synthetic and real-world data, comparing against state-of-the-art algorithms.

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 a representation of the synthesis problems using a novel constraint satisfaction paradigm, satisfiability modulo convex optimization (SMC). We choose SMC because it matches the expressivity needs for our network synthesis. To scale to large problem sizes, we develop a hierarchical synthesis technique that independently synthesizes networks in sub-regions of the deployment area, then combines these. Our experiments show that SMC consistently generates better quality solutions than a baseline synthesis approach based on Mixed Integer Linear Programming (MILP).