Abstract-We model information dissemination as a susceptible-infected epidemic process and formulate a problem to jointly optimize seeds for the epidemic and time varying resource allocation over the period of a fixed duration campaign running on a social network with a given adjacency matrix. Individuals in the network are grouped according to their centrality measure and each group is influenced by an external control function-implemented through advertisements-during the campaign duration. The aim is to maximize an objective function which is a linear combination of the reward due to the fraction of informed individuals at the deadline, and the aggregated cost of applying controls (advertising) over the campaign duration. We also study a problem variant with a fixed budget constraint. We set up the optimality system using Pontryagin's Maximum Principle from optimal control theory and solve it numerically using the forward-backward sweep technique. Our formulation allows us to compare the performance of various centrality measures (pagerank, degree, closeness and betweenness) in maximizing the spread of a message in the optimal control framework. We find that degree-a simple and local measure-performs well on the three social networks used to demonstrate results: scientific collaboration, Slashdot and Facebook. The optimal strategy targets central nodes when the resource is scarce, but noncentral nodes are targeted when the resource is in abundance. Our framework is general and can be used in similar studies for other disease or information spread models-that can be modeled using a system of ordinary differential equations-for a network with a known adjacency matrix.
Kandhway et al. REF modeled the influence maximization problem as a susceptible-infected epidemic process and formulated the problem of selecting the seed set to maximize the VOLUME 7, 2019 influence coverage for a period of time during a campaign on a social network, where users are grouped based on their centrality measure and each group of users is influenced by an optimal control function.
Using Node Centrality and Optimal Control to Maximize Information Diffusion in Social Networks
IEEE Transactions on Systems, Man, and Cybernetics: Systems, Volume: 47, Issue: 7, Pages 1099-1110, July 2017
Computer Science Mathematics Physics