In this article, we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each with a location and a cost), a database of trajectories T , and a budget L , we find a set of billboards within the budget to influence the largest number of trajectories. One core challenge is to identify and reduce the overlap of the influence from different billboards to the same trajectories, while keeping the budget constraint into consideration. We show that this problem is NP-hard and present an enumeration based algorithm with (1-1/e) approximation ratio. However, the enumeration would be very costly when | U | is large. By exploiting the locality property of billboards’ influence, we propose a partition-based framework PartSel. PartSel partitions U into a set of small clusters, computes the locally influential billboards for each cluster, and merges them to generate the global solution. Since the local solutions can be obtained much more efficiently than the global one, PartSel would reduce the computation cost greatly; meanwhile it achieves a non-trivial approximation ratio guarantee. Then we propose a LazyProbe method to further prune billboards with low marginal influence, while achieving the same approximation ratio as PartSel. Next, we propose a branch-and-bound method to eliminate unnecessary enumerations in both PartSel and LazyProbe, as well as an aggregated index to speed up the computation of marginal influence. Experiments on real datasets verify the efficiency and effectiveness of our methods.

中文翻译：

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迈向最佳户外广告位置

在本文中，我们提出并研究了轨迹驱动的有影响力的广告牌放置问题：给定一组广告牌ü（每个都有位置和成本），轨迹数据库吨, 和预算大号，我们在预算范围内找到一组广告牌来影响最多的轨迹。一个核心挑战是识别和减少不同广告牌对相同轨迹的影响的重叠，同时考虑预算约束。我们证明了这个问题是 NP 难的，并提出了一种具有 (1-1/e) 近似比的基于枚举的算法。但是，当 | 时，枚举将非常昂贵。ü| 很大。通过利用广告牌影响的局部性属性，我们提出了一个基于分区的框架 PartSel。PartSel 分区ü成一组小集群，计算每个集群在本地有影响的广告牌，并将它们合并以生成全局解决方案。由于局部解比全局解更高效，PartSel 将大大降低计算成本；同时实现了非平凡的逼近比保证。然后我们提出了一种 LazyProbe 方法来进一步修剪具有低边际影响的广告牌，同时实现与 PartSel 相同的近似比率。接下来，我们提出了一种分支定界方法来消除 PartSel 和 LazyProbe 中不必要的枚举，以及一​​个聚合索引来加快边际影响的计算。在真实数据集上的实验验证了我们方法的效率和有效性。