Distributed Topology Manipulation to Control Epidemic Spreading Over Networks

Abstract

This paper considers the problem of network structure manipulation in the absence of a central coordinator that collects network information and makes decisions. The primary focus is on the spectral radius minimization problem by removing/rewiring links to control epidemic spreading over networks. The resulting optimizations are generally combinatorial and NP-hard. The lack of the central base prevents us from solving such problems in a centralized fashion, thus driving the need for distributed computation and collaborative decision-making to support effective topology modification. In this paper, a distributed estimation scheme involving event-based communication and parallel algorithms is developed to enhance network capability against epidemics. Based on this low-complexity estimation algorithm, fully distributed strategies are proposed to enable individuals to sequentially discern the critical in-network contact, and to implement the desired link operation solely. We further extend the acquisitions to a more flexible framework based on a “coevolutionary networks” picture and discuss the optimality of solutions from an algebraic and topological perspective. Extensive simulation examples are presented to demonstrate the effectiveness of the proposed strategies.