A Billion-Scale Approximation Algorithm for Maximizing Benefit in Viral Marketing

Online social networks have been one of the most effective platforms for marketing and advertising. Through the “world-of-mouth” exchanges, so-called viral marketing, the influence and product adoption can spread from few key influencers to billions of users in the network. To identify those key influencers, a great amount of work has been devoted for the influence maximization (<italic>IM</italic>) problem that seeks a set of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> seed users that maximize the expected influence. Unfortunately, <italic>IM</italic> encloses two impractical assumptions: 1) any seed user can be acquired with the same cost and 2) all users are equally interested in the advertisement. In this paper, we propose a new problem, called <italic>cost-aware targeted viral marketing</italic> ( <italic>CTVM</italic>), to find the most cost-effective seed users, who can influence the most relevant users to the advertisement. Since <italic>CTVM</italic> is NP-hard, we design an efficient <inline-formula> <tex-math notation="LaTeX">$(1- 1/\sqrt {e}-\epsilon )$ </tex-math></inline-formula>-approximation algorithm, named Billion-scale Cost-award Targeted algorithm (BCT), to solve the problem in billion-scale networks. Comparing with <italic>IM</italic> algorithms, we show that <italic>BCT</italic> is both theoretically and experimentally faster than the state-of-the-arts while providing better solution quality. Moreover, we prove that under the linear threshold model, <italic>BCT</italic> is the first <italic>sub-linear time</italic> algorithm for <italic>CTVM</italic> (and <italic>IM</italic>) in dense networks. We carry a comprehensive set of experiments on various real-networks with sizes up to several billion edges in diverse disciplines to show the absolute superiority of <italic>BCT</italic> on both <italic>CTVM</italic> and <italic>IM</italic> domains. Experiments on Twitter data set, containing 1.46 billions of social relations and 106 millions tweets, show that <italic>BCT</italic> can identify key influencers in trending topics in only few minutes.