Billboard Advertising has emerged as an effective out-of-home advertising technique, where the goal is to select a limited number of slots and play advertisement content there, with the hope that it 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. To solve the common-slot variant, we formulate the problem as a multi-submodular cover problem and design a bi-criteria approximation algorithm based on the continuous greedy framework and randomized rounding. For the disjoint-slot variant, we proposed a sampling-based approximation approach along with an efficient primal-dual greedy algorithm that enforces disjointness naturally. Extensive experiments with real-world trajectory and billboard datasets highlight the effectiveness and efficiency of the proposed solution approaches.

翻译：广告牌广告已成为一种有效的户外广告技术，其目标在于选择有限数量的广告位并播放广告内容，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实现影响力最大化？本文研究该问题的一个变体：某商业机构需推广多种产品，且每种产品存在特定的影响力需求。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，使得每种产品的各自影响力需求均得到满足。在另一种问题变体中，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。针对共享广告位变体，我们将问题形式化为多子模覆盖问题，并基于连续贪心框架与随机舍入设计了一种双准则近似算法。针对互斥广告位变体，我们提出了一种基于采样的近似方法，并结合能自然保证互斥性的高效原始对偶贪心算法。基于真实世界轨迹与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。