Continuous Profit Maximization: A Study of Unconstrained Dr-Submodular Maximization

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 profit from influence spread. We extend PM that under general strategy, form continuous (CPM-MS) problem, whose domain on integer lattices. The objective function our CPM-MS dr-submodular, but non-monotone. It typical case unconstrained dr-submodular (UDSM) take it starting point, we study UDSM systematically this paper, very different those existing researcher. First, introduce lattice-based double greedy algorithm, can obtain constant approximation guarantee. However, there strict unrealistic condition requiring value non-negative whole domain, or else no theoretical bounds. Thus, propose technique, called iterative pruning. shrink search space effectively, thereby greatly increasing possibility satisfying smaller without losing ratio. Then, overcome difficulty estimate CPM-MS, adopt reverse sampling strategies, combine with greedy, including pruning, its performance reducing running time. entire process be considered framework solve especially applying networks. Finally, conduct experiments several real datasets evaluate effectiveness efficiency proposed algorithms.