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 nearoptimal approximation factor of (1 − 1 e − ǫ), for any ǫ > 0, in time O((m + n)ǫ logn). Our algorithm is runtime-optimal (up to a logarithmic factor) and substantially improves upon the previously best-known algorithms which run in time Ω(mnk · POLY(ǫ)). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O(β(m+n) log n) steps for some β < 1 (which can depend on n), then it returns a solution with approximation factor O(β). Finally, we show that this runtime is optimal (up to logarithmic factors) for any β and fixed seed size k. Microsoft Research New England. Computer and Information Science, University of Pennsylvania. Now in The Laboratory for Information and Decision Systems, Massachusetts Institute of Technology. Microsoft Research New England. Microsoft Research New England.