What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks

TL;DR

This paper introduces a new strategy for controlling diffusion in networks by minimizing maximum cutwidth, providing theoretical bounds and demonstrating superior performance over existing methods.

Contribution

The paper develops a novel DRA strategy called Maximum Cutwidth Minimization, linking network arrangement properties to diffusion control effectiveness.

Findings

Maximum cutwidth effectively predicts diffusion control quality.

Maximum Cutwidth Minimization outperforms existing strategies in simulations.

Theoretical bounds relate maximum cutwidth to diffusion extinction time.

Abstract

In this paper, we analyze the quality of a large class of simple dynamic resource allocation (DRA) strategies which we name priority planning. Their aim is to control an undesired diffusion process by distributing resources to the contagious nodes of the network according to a predefined priority-order. In our analysis, we reduce the DRA problem to the linear arrangement of the nodes of the network. Under this perspective, we shed light on the role of a fundamental characteristic of this arrangement, the maximum cutwidth, for assessing the quality of any priority planning strategy. Our theoretical analysis validates the role of the maximum cutwidth by deriving bounds for the extinction time of the diffusion process. Finally, using the results of our analysis, we propose a novel and efficient DRA strategy, called Maximum Cutwidth Minimization, that outperforms other competing strategies in our simulations.