Submodularity in Input Node Selection for Networked Systems

TL;DR

This paper explores how submodular optimization can be used to efficiently select input nodes in networked systems, improving control strategies for complex interconnected systems like power grids and social networks.

Contribution

It introduces submodular optimization methods tailored for input node selection, leveraging physical dynamics to develop efficient algorithms with provable guarantees.

Findings

Submodular structures are identified in various physical network dynamics.

Efficient algorithms with provable bounds are developed for input node selection.

Open problems in the application of submodularity to network control are discussed.

Abstract

Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical infrastructures such as power grids, transportation systems, and the Internet, and social networks. The growing importance of such systems has led to an interest in control of networks to ensure performance, stability, robustness, and resilience. A widely-studied method for controlling networked systems is to directly control a subset of input nodes, which then steer the remaining nodes to their desired states. This article presents submodular optimization approaches for input node selection in networked systems. Submodularity is a property of set functions that enables the development of computationally tractable algorithms with provable optimality bounds. For a variety of physically relevant systems, the physical dynamics have submodular structures that can be exploited to develop efficient input selection algorithms. This article will describe these structures and the resulting algorithms, as well as discuss open problems.