History Sensitive Cascade Model

Diffusion is a process by which information, viruses, ideas, or new behavior spread over social networks. Traditional diffusion models are history insensitive, i.e. only giving activated nodes a one-time chance to activate each of its neighboring nodes with some probability. But history dependent interactions between people are often observed in the real world. This paper proposes the History Sensitive Cascade Model HSCM, a model of information cascade through a network over time. The authors consider the "activation" problem of finding the probability of that a particular node receives information given that some nodes are initially informed. In this paper it is also proven that selecting a set of k nodes with greatest expected influence is NP-hard, and results from submodular functions are used to provide a greedy approximation algorithm with a 1-1/e-e lower bound, where e depends polynomially on the precision of the solution to the "activation" problem. Finally, experiments are performed comparing the greedy algorithm to three other approximation algorithms.