An Upper Bound based Greedy Algorithm for Mining Top-k Influential Nodes in Social Networks

Influence maximization [4] is NP-hard under the Linear Threshold (LT) model, where a line of greedy algorithms have been proposed. The simple greedy algorithm [4] guarantees accuracy rate of 1 - 1/e to the optimal solution; the advanced greedy algorithm, e.g., the CELF algorithm [6], runs 700 times faster by exploiting the submodular property of the spread function. However, both models lack efficiency due to heavy Monte-Carlo simulations during estimating the spread function. To this end, in this paper we derive an upper bound for the spread function under the LT model. Furthermore, we propose an efficient UBLF algorithm by incorporating the bound into CELF. Experimental results demonstrate that UBLF, compared with CELF, reduces about 98.9% Monte-Carlo simulations and achieves at least 5 times speed-raising when the size of seed set is small.