Maximizing Social Influence in Nearly Optimal Time

Abstract

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)kǫ −2 log n). Our algorithm is runtime-optimal (up to a logarithmic factor) with respect to network size, and substantially improves upon the previously best-known algorithms which run in time Ω(mnk · POLY(ǫ −1 )). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O(β(m + n)k 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.

Detecting Critical Links in Complex Network to Maintain Information Flow/Reachability

“…Many studies were also made on exploring effective strategies for reducing the spread of infection by removing nodes in a network [1,5,6,25]. Moreover, we note that the contamination minimization problem can be converse to the influence maximization problem, which has recently attracted much interest in the field of social network mining [16,19,23,8,9,15,3,29,31].…”

“…The first one is a high-energy physics citation network from the e-print arXiv 3 , which covers all the citations within a dataset of 34, 546 papers (nodes) with 421, 578 citations (links). If a paper u cites paper v, the network contains a directed link from u to v. The second one is a sequence of snapshots of the Gnutella peer-to-peer file sharing network from August 2002 4 .…”

Speeding-up node influence computation for huge social networks

“…Since then, many researchers have proposed various techniques for improving the efficiency in finding high-quality approximate solutions [8][9][10]13,17,20,24,30]. Recently, Borgs et al [4] provided a fast algorithm running in quasilinear time, and mathematically proved its high performance. Song et al [27] introduced a diffusion model to accommodate link weights, and investigated the influence maximization problem for a mobile social network where individuals communicate with one another using mobile phones.…”

Influence maximisation beyond organisational boundaries

“…Efficiently choosing such influential individuals, or influence maximisation (IM), is a well-studied problem in the computer science literature [4]- [7]. This line of work proposes algorithms that identify influential individuals and predict network spread with some operational guarantees given a fully known network.…”