Growing Controllable Networks via Whiskering and Submodular Optimization

TL;DR

This paper introduces a method for growing networks through whiskering and submodular optimization, ensuring controllability is preserved while optimizing network properties like connectivity.

Contribution

It presents a novel network growth technique called whiskering, proves its controllability preservation, and applies submodular optimization for effective network augmentation.

Findings

Whiskering preserves network controllability.

Submodular optimization effectively improves network connectivity.

The methods enable controlled network growth with optimized properties.

Abstract

The topology of a network directly influences the behaviour and controllability of dynamical processes on that network. Therefore, the design of network topologies is an important area of research when examining the control of distributed systems. We discuss a method for growing networks known as whiskering, as well as generalizations of this process, and prove that they preserve controllability. We then use techniques from submodular optimization to analyze optimization algorithms for adding new nodes to a network to optimize certain objectives, such as graph connectivity.