Towards Time-Discounted Influence Maximization

The classical influence maximization (IM) problem in social networks does not distinguish between whether a campaign gets viral in a week or in a year. From the practical standpoint, however, campaigns for a new technology or an upcoming movie must be spread as quickly as possible, otherwise they will be obsolete. To this end, we formulate and investigate the novel problem of maximizing the time-discounted influence spread in a social network, that is, the campaigner is interested in both "when" and "how likely" a user would be influenced. In particular, we assume that the campaigner has a utility function which monotonically decreases with the time required for a user to get influenced, since the activation of the seed nodes. The problem that we solve in this paper is to maximize the expected aggregated value of this utility function over all network users. This is a novel and relevant problem that, surprisingly, has not been studied before. Time-discounted influence maximization (TDIM), being a generalization of the classical IM, still remains NP-hard. However, our main contribution is to prove the sub-modularity of the objective function for any monotonically decreasing function of time, under a variety of influence cascading models, e.g., the independent cascade, linear threshold, and maximum influence arborescence models, thereby designing approximate algorithms with theoretical performance guarantees. We also illustrate that the existing optimization techniques (e.g., CELF) for influence maximization are more efficient over TDIM. Our experimental results demonstrate the effectiveness of our solutions over several baselines including the classical influence maximization algorithms.