Influential Slot and Tag Selection in Billboard Advertisement

The selection of influential billboard slots remains an important problem in billboard advertisements. Existing studies on this problem have not considered the case of context-specific influence probability. To bridge this gap, in this paper, we introduce the Context Dependent Influential Billboard Slot Selection Problem. First, we show that the problem is NP-hard. We also show that the influence function holds the bi-monotonicity, bi-submodularity, and non-negativity properties. We propose an orthant-wise Stochastic Greedy approach to solve this problem. We show that this method leads to a constant-factor approximation guarantee. Subsequently, we propose an orthant-wise Incremental and Lazy Greedy approach. In a generic sense, this is a method for maximizing a bi-submodular function under the cardinality constraint, which may also be of independent interest. We analyze the performance guarantee of this algorithm as well as time and space complexity. The proposed solution approaches have been implemented with real-world billboard and trajectory datasets. We compare the performance of our method with several baseline methods, and the results are reported. Our proposed orthant-wise stochastic greedy approach leads to significant results when the parameters are set properly with reasonable computational overhead.