* Masahiro Kimura, Kazumi Saito, Ryohei Nakano.*

We consider the combinatorial optimization problem of finding the most influential nodes on a large-scale social network for two widely-used fundamental stochastic diffusion models. It was shown that a natural greedy strategy can give a good approximate solution to this optimization problem. However, a conventional method under the greedy algorithm needs a large amount of computation, since it estimates the marginal gains for the expected number of nodes influenced by a set of nodes by simulating the random process of each model many times. In this paper, we propose a method of efficiently estimating all those quantities on the basis of bond percolation and graph theory, and apply it to approximately solving the optimization problem under the greedy algorithm. Using real-world large-scale networks including blog networks, we experimentally demonstrate that the proposed method can outperform the conventional method, and achieve a large reduction in computational cost.

*Subjects: *12. Machine Learning and Discovery;
3.4 Probabilistic Reasoning

*Submitted: *Apr 15, 2007

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