Influence maximization on undirected graphs: Toward closing the (1-1/e) gap

摘要: We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ > 0) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model, the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem …