Profit maximization in social networks and non-monotone DR-submodular maximization

In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions lattice have been defined submodular property that is similar to submodularity of set functions. a further extended concept for functions lattice, which captures diminishing return property. Such find many applications in machine learning, social networks, wireless etc. The techniques can be applied maximization, e.g., double greedy algorithm has 1/2-approximation ratio, whose running time O(nB), where n size ground set, B bound coordinate. our study, design 1/2-approximate binary search algorithm, and prove its complexity O(nlog⁡B), significantly improves time. Specifically, consider application profit problem networks with bipartite model, goal maximize net gained from product promoting activity, difference influence gain cost. We objective apply verify effectiveness.