Maximizing Social Influence in Nearly Optimal Time

Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network diffusion. Runtime is a primary consideration for this problem due to the massive size of the relevant input networks. We provide a fast algorithm for the influence maximization problem, obtaining the near-optimal approximation factor of (1 - 1/e - epsilon), for any epsilon > 0, in time O ( (m+n) k log (n) / epsilon²). Our algorithm is runtime-optimal (up to a logarithmic factor) and substantially improves upon the previously best-known algorithms which run in time Omega (mnk POLY (1/epsilon) ). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O (beta (m+n) k log (n) ) steps for some beta < 1 (which can depend on n), then it returns a solution with approximation factor O (beta). Finally, we show that this runtime is optimal (up to logarithmic factors) for any beta and fixed seed size k.