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

Abstract

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 ( IM ) problem that seeks a set of $k$ seed users that maximize the expected influence. Unfortunately, IM 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 cost-aware targeted viral marketing ( CTVM ), to find the most cost-effective seed users, who can influence the most relevant users to the advertisement. Since CTVM is NP-hard, we design an efficient $(1- 1/\sqrt {e}-\epsilon )$ -approximation algorithm, named Billion-scale Cost-award Targeted algorithm (BCT), to solve the problem in billion-scale networks. Comparing with IM algorithms, we show that BCT 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, BCT is the first sub-linear time algorithm for CTVM (and IM ) 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 BCT on both CTVM and IM domains. Experiments on Twitter data set, containing 1.46 billions of social relations and 106 millions tweets, show that BCT can identify key influencers in trending topics in only few minutes.