Billboard Advertisement has emerged as an effective out-of-home advertisement technique where the goal is to select a limited number of slots and play advertisement content over there with the hope that this will be observed by many people, and effectively, a significant number of them will be influenced towards the brand. Given a trajectory and a billboard database and a positive integer $k$, how can we select $k$ highly influential slots to maximize influence? In this paper, we study a variant of this problem where a commercial house wants to make a promotion of multiple products, and there is an influence demand for each product. We have studied two variants of the problem. In the first variant, our goal is to select $k$ slots such that the respective influence demand of each product is satisfied. In the other variant of the problem, we are given with $\ell$ integers $k_1,k_2, \ldots, k_{\ell}$, the goal here is to search for $\ell$ many set of slots $S_1, S_2, \ldots, S_{\ell}$ such that for all $i \in [\ell]$, $|S_{i}| \leq k_i$ and for all $i \neq j$, $S_i \cap S_j=\emptyset$ and the influence demand of each of the products gets satisfied. We model the first variant of the problem as a multi-submodular cover problem and the second variant as its generalization. For solving the first variant, we adopt the bi-criteria approximation algorithm, and for the other variant, we propose a sampling-based approximation algorithm. Extensive experiments with real-world trajectory and billboard datasets highlight the effectiveness and efficiency of the proposed solution approach.

翻译：广告牌广告已成为一种有效的户外广告技术，其目标是在有限数量的广告位播放广告内容，以期被众多人群观看，并有效促使其中相当数量的人受到品牌影响。给定轨迹数据、广告牌数据库以及一个正整数$k$，我们应如何选择$k$个高影响力广告位以最大化影响力？本文研究该问题的一个变体：某商业机构希望推广多种产品，且每种产品均有特定的影响力需求。我们研究了该问题的两种变体。在第一种变体中，我们的目标是选择$k$个广告位，使得每种产品各自的影响力需求均得到满足。在另一种变体中，给定$\ell$个整数$k_1,k_2, \ldots, k_{\ell}$，目标是寻找$\ell$组广告位集合$S_1, S_2, \ldots, S_{\ell}$，使得对于所有$i \in [\ell]$满足$|S_{i}| \leq k_i$，且对于所有$i \neq j$有$S_i \cap S_j=\emptyset$，同时每种产品的影响力需求均得到满足。我们将第一种问题变体建模为多子模覆盖问题，第二种变体则建模为其推广形式。针对第一种变体，我们采用双准则近似算法进行求解；针对第二种变体，我们提出一种基于采样的近似算法。基于真实世界轨迹和广告牌数据集的大量实验验证了所提解决方案的有效性与高效性。