Minimizing cost for influencing target groups in social network: A model and algorithmic approach

Abstract

Stimulated by practical applications arising from economics, viral marketing, and elections, this paper studies the problem of Groups Influence with Minimum cost (GIM), which aims to find a seed set with the smallest cost that can influence all target groups in a social network, where each user is assigned a cost and a score and a group of users is influenced if the total score of influenced users in the group is at least a certain threshold. As the group influence function, defined as the number of influenced groups or users, is neither submodular nor supermodular, theoretical bounds on the quality of solutions returned by the well-known greedy approach may not be guaranteed.In this work, two efficient algorithms with theoretical guarantees for tackling the GIM problem, named Groups Influence Approximation (GIA) and Exact Groups Influence (EGI), are proposed. GIA is a bi-criteria polynomial-time approximation algorithm and EGI is an (almost) exact algorithm; both can return good approximate solutions with high probability. The novelty of our approach lies in two aspects. Firstly, a novel group reachable reverse sample concept is proposed to estimate the group influence function within an error bound. Secondly, a framework algorithmic is designed to find serial candidate solutions with checking theoretical guarantees at the same time. Besides theoretical results, extensive experiments conducted on real social networks show our algorithms' performance. In particular, both EGI and GIA provide the solution quality several times better, while GIA is up to 800 times faster than the state-of-the-art algorithms.