Optimal Resource Allocation Over Time and Degree Classes for Maximizing Information Dissemination in Social Networks

TL;DR

This paper develops an optimal control framework for allocating resources over time and degree classes in social networks to maximize information spread, considering network topology and costs, with applications in marketing and political campaigns.

Contribution

It introduces a novel optimal control model for resource allocation in social networks, incorporating degree classes, network topology, and cost constraints, with proven existence and structural properties of solutions.

Findings

Resource allocation strategies vary with network topology and system parameters.

Optimal strategies outperform heuristic approaches significantly.

The model is applicable to real-world social networks despite assumptions.

Abstract

We study the optimal control problem of allocating campaigning resources over the campaign duration and degree classes in a social network. Information diffusion is modeled as a Susceptible-Infected epidemic and direct recruitment of susceptible nodes to the infected (informed) class is used as a strategy to accelerate the spread of information. We formulate an optimal control problem for optimizing a net reward function, a linear combination of the reward due to information spread and cost due to application of controls. The time varying resource allocation and seeds for the epidemic are jointly optimized. A problem variation includes a fixed budget constraint. We prove the existence of a solution for the optimal control problem, provide conditions for uniqueness of the solution, and prove some structural results for the controls (e.g. controls are non-increasing functions of time). The solution technique uses Pontryagin's Maximum Principle and the forward-backward sweep algorithm (and its modifications) for numerical computations. Our formulations lead to large optimality systems with up to about 200 differential equations and allow us to study the effect of network topology (Erdos-Renyi/scale-free) on the controls. Results reveal that the allocation of campaigning resources to various degree classes depends not only on the network topology but also on system parameters such as cost/abundance of resources. The optimal strategies lead to significant gains over heuristic strategies for various model parameters. Our modeling approach assumes uncorrelated network, however, we find the approach useful for real networks as well. This work is useful in product advertising, political and crowdfunding campaigns in social networks.