On non-progressive spread of influence through social networks - Fazli, MohammadAmin; Ghodsi, Mohammad; Habibi, Jafar; Jalaly, Pooya; Mirrokni, Vahab; Sadeghian, Sina (Theoretical computer science, 2014)
The spread of influence in social networks is studied in two main categories: progressive models and non-progressive models (see, e.g., the seminal work of Kempe et al. [8]). While the progressive models are suitable for modeling the spread of influence in monopolistic settings, non-progressive models are more appropriate for non-monopolistic settings, e.g., modeling diffusion of two competing technologies over a social network. Despite the extensive work on progressive models, non-progressive models have not been considered as much. In this paper, we study the spread of influence in the non-progressive model under the strict majority threshold: given a graph G with a set of initially infected nodes, each of which gets infected at time τ iff a majority of its neighbors are infected at time τ−1. Our goal in the MinPTS problem is to find a minimum-cardinality initial set of infected nodes that would eventually converge to the steady state where all nodes of G are infected. We prove that while the MinPTS problem is NP-complete for a restricted family of graphs, it admits a constant-factor approximation algorithm for power-law graphs. We do so by proving the lower and upper bounds on the optimal solution of the MinPTS problem in terms of the minimum and maximum degrees of nodes in the graph. The upper bound is achieved in turn by applying a natural greedy algorithm. Our experimental evaluation of the greedy algorithm also shows its superior performance compared to other algorithms for a set of real-world graphs as well as the random power-law graphs. Finally, we study the convergence properties of these algorithms and show that the non-progressive model converges in at most O(|E(G)|) steps.