Profit Maximization using Social Networks in Two-Phase Setting

Now-a-days, \emph{Online Social Networks} have been predominantly used by commercial houses for viral marketing where the goal is to maximize profit. In this paper, we study the problem of Profit Maximization in the two\mbox{-}phase setting. The input to the problem is a \emph{social network} where the users are associated with a cost and benefit value, and a fixed amount of budget splitted into two parts. Here, the cost and the benefit associated with a node signify its incentive demand and the amount of benefit that can be earned by influencing that user, respectively. The goal of this problem is to find out the optimal seed sets for both phases such that the aggregated profit at the end of the diffusion process is maximized. First, we develop a mathematical model based on the \emph{Independent Cascade Model} of diffusion that captures the aggregated profit in an \emph{expected} sense. Subsequently, we show that selecting an optimal seed set for the first phase even considering the optimal seed set for the second phase can be selected efficiently, is an $\textsf{NP}$-Hard Problem. Next, we propose two solution methodologies, namely the \emph{single greedy} and the \emph{double greedy} approach for our problem that works based on marginal gain computation. A detailed analysis of both methodologies has been done to understand their time and space requirements. We perform an extensive set of experiments to demonstrate the effectiveness and efficiency of the proposed approaches with real-world datasets. From the experiments, we observe that the proposed solution approaches lead to more profit compared to the baseline methods and in particular, the double greedy approach leads to up to $5 \%$ improvement compared to its single\mbox{-}phase counterpart.