Details of Research Outputs

Profit maximization (PM) is to select a subset of users as seeds for viral marketing in online social networks, which balances between the cost and the profit from influence spread. We extend PM to formulate a continuous PM under the general marketing strategies (CPM-MS) problem, whose domain is on integer lattices. The objective function of our CPM-MS is dr-submodular, but nonmonotone. It is a typical case of unconstrained dr-submodular maximization (UDSM) problem, and taking it as a starting point, we study UDSM systematically in this article, which is very different from those studied by existing researchers. First, we introduce the lattice-based double greedy algorithm, which can obtain a constant approximation guarantee. However, there is a strict and unrealistic condition that requiring the objective value is nonnegative on the whole domain or else no theoretical bounds. Thus, we propose a lattice-based iterative pruning technique. It can shrink the search space effectively, thereby greatly increasing the possibility of satisfying the nonnegative objective function on this smaller domain without losing approximation ratio. Then, to overcome the difficulty to estimate the objective value of CPM-MS, we adopt reverse sampling strategies and combine it with lattice-based double greedy, including pruning, without losing its performance but reducing its running time. The entire process can be considered as a general framework to solve the UDSM problem, especially for applying to social networks. Finally, we conduct experiments on several real data sets to evaluate the effectiveness and efficiency of our proposed algorithms.