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Influence Maximization (IM), which aims to select a set of users from a social network to maximize the expected number of influenced users, has recently received significant attention for mass communication and commercial marketing. Existing research efforts dedicated to the IM problem depend on a strong assumption: the selected seed users are willing to spread the information after receiving benefits from a company or organization. In reality, however, some seed users may be reluctant to spread the information, or need to be paid higher to be motivated. Furthermore, the existing IM works pay little attention to capture user's influence propagation in the future period as well. In this paper, we target a new research problem, named Reconnecting Top-l Relationships (RTlR) query, which aims to find l number of previous existing relationships but being stranged later, such that reconnecting these relationships will maximize the expected benefit of influenced users by the given group in a future period. We prove that the RTlR problem is NP-hard. An efficient greedy algorithm is proposed to answer the RTlR queries with the influence estimation technique and the well-chosen link prediction method to predict the near future network structure. We also design a pruning method to reduce unnecessary probing from candidate edges. Further, a carefully designed order-based algorithm is proposed to accelerate the RTlR queries. Finally, we conduct extensive experiments on real-world datasets to demonstrate the effectiveness and efficiency of our proposed methods.