Submodularity in Action: From Machine Learning to Signal Processing Applications

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: $(i)$ relaxation into the continuous domain to obtain an approximate solution, or $(ii)$ development of a tailored algorithm that applies directly in the discrete domain. In both approaches, worst-case performance guarantees are often hard to establish. Furthermore, they are often complex, thus not practical for large-scale problems. In this paper, we show how certain scenarios lend themselves to exploiting submodularity so as to construct scalable solutions with provable worst-case performance guarantees. We introduce a variety of submodular-friendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization. With a mixture of theory and practice, we present different flavors of submodularity accompanying illustrative real-world case studies from modern SP and ML. In all cases, optimization algorithms are presented, along with hints on how optimality guarantees can be established

Real-Time and Energy-Efficient Routing for Industrial Wireless Sensor-Actuator Networks

With the emergence of industrial standards such as WirelessHART, process industries are adopting Wireless Sensor-Actuator Networks (WSANs) that enable sensors and actuators to communicate through low-power wireless mesh networks. Industrial monitoring and control applications require real-time communication among sensors, controllers and actuators within end-to-end deadlines. Deadline misses may lead to production inefficiency, equipment destruction to irreparable financial and environmental impacts. Moreover, due to the large geographic area and harsh conditions of many industrial plants, it is labor-intensive or dan- gerous to change batteries of field devices. It is therefore important to achieve long network lifetime with battery-powered devices. This dissertation tackles these challenges and make a series of contributions. (1) We present a new end-to-end delay analysis for feedback control loops whose transmissions are scheduled based on the Earliest Deadline First policy. (2) We propose a new real-time routing algorithm that increases the real-time capacity of WSANs by exploiting the insights of the delay analysis. (3) We develop an energy-efficient routing algorithm to improve the network lifetime while maintaining path diversity for reliable communication. (4) Finally, we design a distributed game-theoretic algorithm to allocate sensing applications with near-optimal quality of sensing