We introduce the history sensitive cascade model, a model of information cascade through a network over time. We consider the 'activation' problem of finding the probability of a particular node receiving information given that some nodes are initially informed. Finally, we prove that selecting a set of k nodes with greatest expected influence is NP-hard, and use results from submodular functions to provide a greedy approximation algorithm with a 1 − 1/e − lower bound, where depends polynomially on the precision of the solution to the 'activation' problem. We perform experiments in order to compare the greedy algorithm to three other approximation algorithms.

We introduce the history sensitive cascade model, a model of information cascade through a network over time. We consider the 'activation' problem of finding the probability of a particular node receiving information given that some nodes are initially informed. Finally, we prove that selecting a set of k nodes with greatest expected influence is NP-hard, and use results from submodular functions to provide a greedy approximation algorithm with a 1 − 1/e − lower bound, where depends polynomially on the precision of the solution to the 'activation' problem. We perform experiments in order to compare the greedy algorithm to three other approximation algorithms.