Influence Maximization In Near-Linear Time: A Martingale Approach

Abstract

Given a social network <i>G</i> and a positive integer <i>k</i>, the <i>influence maximization</i> problem asks for <i>k</i> nodes (in <i>G</i>) whose adoptions of a certain idea or product can trigger the largest expected number of follow-up adoptions by the remaining nodes. This problem has been extensively studied in the literature, and the state-of-the-art technique runs in <i>O</i>((<i>k</i>+<i>l</i>) (<i>n+m</i>) log <i>n</i> ε²) expected time and returns a (1-1 <i>e</i>-ε)-approximate solution with at least 1 - 1/<i>n</i>^l probability. This paper presents an influence maximization algorithm that provides the same worst-case guarantees as the state of the art, but offers significantly improved empirical efficiency. The core of our algorithm is a set of estimation techniques based on <i>martingales</i>, a classic statistical tool. Those techniques not only provide accurate results with small computation overheads, but also enable our algorithm to support a larger class of information diffusion models than existing methods do. We experimentally evaluate our algorithm against the states of the art under several popular diffusion models, using real social networks with up to 1.4 billion edges. Our experimental results show that the proposed algorithm consistently outperforms the states of the art in terms of computation efficiency, and is often orders of magnitude faster.