Billboard advertising is a popular out-of-home advertising technique adopted by commercial houses. Companies own billboards and offer them to commercial houses on a payment basis. Given a database of billboards with slot information, we want to determine which k slots to choose to maximize influence. We call this the INFLUENTIAL BILLBOARD SLOT SELECTION (IBSS) Problem and pose it as a combinatorial optimization problem. We show that the influence function considered in this paper is non-negative, monotone, and submodular. The incremental greedy approach based on the marginal gain computation leads to a constant factor approximation guarantee. However, this method scales very poorly when the size of the problem instance is very large. To address this, we propose a spatial partitioning and pruned submodularity graph-based approach that is divided into the following three steps: preprocessing, pruning, and selection. We analyze the proposed solution approaches to understand their time, space requirement, and performance guarantee. We conduct extensive set of experiments with real-world datasets and compare the performance of the proposed solution approaches with the available baseline methods. We observe that the proposed approaches lead to more influence than all the baseline methods within reasonable computational time.

翻译：广告牌广告是一种流行的户外广告技术，被商业机构广泛采用。公司拥有广告牌并通过付费方式提供给商业机构使用。给定一个包含插槽信息的广告牌数据库，我们需要确定选择哪些k个插槽以最大化影响力。我们将此问题定义为"有影响力广告牌插槽选择"（IBSS）问题，并将其表述为一个组合优化问题。我们证明了本文考虑的影响力函数是非负、单调且子模的。基于边际增益计算的增量贪心方法可获得常数因子近似保证。然而，当问题实例规模非常大时，该方法的扩展性极差。为解决此问题，我们提出了一种基于空间划分和剪枝子模图的方法，该方法分为以下三个步骤：预处理、剪枝和选择。我们分析了所提出的解决方案，以理解其时间、空间需求以及性能保证。我们利用真实数据集进行了大量实验，并将所提出的解决方案与现有基线方法的性能进行了比较。我们观察到，在合理的计算时间内，所提出的方法比所有基线方法产生了更大的影响力。