Trajectory-driven Influential Billboard Placement

TL;DR

This paper addresses the complex problem of placing billboards to influence the maximum number of trajectories within a budget, proposing a scalable partition-based solution with strong approximation guarantees.

Contribution

It introduces PartSel, a partition-based framework leveraging locality to efficiently approximate optimal billboard placement, and proposes LazyProbe for further pruning.

Findings

PartSel significantly reduces computation time compared to enumeration.

The methods achieve high influence coverage within budget constraints.

Experimental results validate the efficiency and effectiveness of the proposed algorithms.

Abstract

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.