Influence maximization, fundamental for word-of-mouth marketing and viral marketing, aims to find a set of seed nodes maximizing influence spread on social network. Early methods mainly fall into two paradigms with certain benefits and drawbacks: (1)Greedy algorithms, selecting seed nodes one by one, give a guaranteed accuracy relying on the accurate approximation of influence spread with high computational cost; (2)Heuristic algorithms, estimating influence spread using efficient heuristics, have low computational cost but unstable accuracy. We first point out that greedy algorithms are essentially finding a self-consistent ranking, where nodes ranks are consistent with their ranking-based marginal influence spread. This insight motivates us to develop an iterative ranking framework, i.e., IMRank, to efficiently solve influence maximization problem under independent cascade model. Starting from an initial ranking, e.g., one obtained from efficient heuristic algorithm, IMRank finds a self-consistent ranking by reordering nodes iteratively in terms of their ranking-based marginal influence spread computed according to current ranking. We also prove that IMRank definitely converges to a self-consistent ranking starting from any initial ranking. Furthermore, within this framework, a last-to-first allocating strategy and a generalization of this strategy are proposed to improve the efficiency of estimating ranking-based marginal influence spread for a given ranking. In this way, IMRank achieves both remarkable efficiency and high accuracy by leveraging simultaneously the benefits of greedy algorithms and heuristic algorithms. As demonstrated by extensive experiments on large scale real-world social networks, IMRank always achieves high accuracy comparable to greedy algorithms, with computational cost reduced dramatically, even about $10-100$ times faster than other scalable heuristics.
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