Maximizing Algebraic Connectivity of Constrained Graphs in Adversarial Environments

TL;DR

This paper develops methods to maximize network connectivity through topology design under constraints and adversarial threats, introducing non-greedy optimization techniques and heuristics for protection strategies.

Contribution

It formulates a nonconvex binary optimization problem for edge addition under constraints and proposes three heuristic algorithms for adversarial edge protection.

Findings

The proposed methods effectively increase algebraic connectivity in simulations.

Heuristic algorithms outperform naive strategies in adversarial scenarios.

The approach accommodates complex constraints and adversarial uncertainties.

Abstract

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design problem of adding edges to an initial graph, which introduces a nonconvex binary decision variable, in addition to subjugation to general convex constraints on the feasible edge set. Unlike previous methods, our method is justifiably not greedy and capable of accommodating these additional constraints. We also study a scenario in which a coordinator must selectively protect edges of the network from a chance of failure due to a physical disturbance or adversarial attack. The coordinator needs to strategically respond to the adversary's action without presupposed knowledge of the adversary's feasible attack actions. We propose three heuristic algorithms for the coordinator to accomplish the objective and identify worst-case preventive solutions. Each algorithm is shown to be effective in simulation and we provide some discussion on their compared performance.