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 -- ε), for any ε > 0, in time O((m + n)ε-3 log n). 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(ε-1)). 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.