Social Influence Maximization in Hypergraphs

This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold diffusion model defined on an input graph with node thresholds, quantifying the hardness to influence each node. The goal is to find the smaller set of items that can influence the whole network according to the diffusion model defined. This study generalizes the TSS problem on networks characterized by many-to-many relationships modeled via hypergraphs. Specifically, we introduce a linear threshold diffusion process on such structures, which evolves as follows. Let H=(V,E) be a hypergraph. At the beginning of the process, the nodes in a given set S⊆V are influenced. Then, at each iteration, (i) the influenced hyperedges set is augmented by all edges having a sufficiently large number of influenced nodes; (ii) consequently, the set of influenced nodes is enlarged by all the nodes having a sufficiently large number of already influenced hyperedges. The process ends when no new nodes can be influenced. Exploiting this diffusion model, we define the minimum Target Set Selection problem on hypergraphs (TSSH). Being the problem NP-hard (as it generalizes the TSS problem), we introduce four heuristics and provide an extensive evaluation on real-world networks.

Preprocessing Rules for Target Set Selection in Complex Networks

In the Target Set Selection (TSS) problem, we want to find the minimum set of individuals in a network to spread information across the entire network. This problem is NP-hard, so find good strategies to deal with it, even for a particular case, is something of interest. We introduce preprocessing rules that allow reducing the size of the input without losing the optimality of the solution when the input graph is a complex network. Such type of network has a set of topological properties that commonly occurs in graphs that model real systems. We present computational experiments with real-world complex networks and synthetic power law graphs. Our strategies do particularly well on graphs with power law degree distribution, such as several real-world complex networks. Such rules provide a notable reduction in the size of the problem and, consequently, gains in scalability.