轨迹驱动的影响力广告牌布局
Trajectory-driven Influential Billboard Placement
摘要：
在本文中，我们提出和研究的问题，有影响力的广告牌的位置：给定一组广告牌$U$（每个位置和成本），一个数据库的轨迹$\mathcal{T}$和预算$L$，找到一组广告牌的预算内影响的最大数量的轨迹。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，同时考虑到预算限制。我们证明了这个问题是NP-难的，并提出了一个基于枚举的算法与$(1-1/e)$逼近比。但是，当$|U|$很大时，枚举的开销会很大。通过利用广告牌影响的局部性，我们提出了一个基于划分的框架PartSel。PartSel将$U$划分为一组小集群，计算每个集群的本地影响力广告牌，并将它们合并以生成全局解决方案。由于局部解的获得比全局解的获得效率高得多，PartSel算法在保证非平凡逼近比的同时，大大降低了计算量.然后，我们提出了一个LazyProbe方法，以进一步修剪广告牌的边际影响力低，同时达到相同的近似比PartSel。在真实数据集上的实验验证了该方法的有效性。
英文摘要：
In this paper 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 $\mathcal{T}$ and a budget $L$, 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 should 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 efficient than the global one, PartSel should 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. Experiments on real datasets verify the efficiency and effectiveness of our methods.
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