Earned benefit maximization in social networks under budget constraint

Given a social network where the users are associated with non-uniform selection cost, the problem of Budgeted Influence Maximization (BIM in short) asks for selecting a subset of the nodes within an allocated budget for initial activation, such that due to the cascading effect, influence in the network is maximized. In this paper, we study this problem with a variation, where a subset of the users are marked as target users, each of them is assigned with a benefit and this can be earned by influencing them. The goal here is to maximize the earned benefit by initially activating a set of nodes within the budget. This problem is referred to as the Earned Benefit Maximization Problem. First, we show that this problem is NP-Hard and the benefit function follows the monotonicity, sub-modularity property under the Independent Cascade Model of diffusion. We propose an incremental greedy strategy for this problem and show, with minor modification it gives (1 - 1 root e)-factor approximation guarantee on the earned benefit. Next, by exploiting the sub-modularity property of the benefit function, we improve the efficiency of the proposed greedy algorithm. Then, we propose a hop-based heuristic method, which works based on the computation of the 'expected earned benefit'. Finally, we perform a series of extensive experiments with four publicly available, real-life social network datasets. From the experiments, we observe that the seed sets selected by the proposed algorithms can achieve more benefit compared to many existing methods. Particularly, the hop-based approach is found to be more efficient than the other ones for solving this problem.