Influential Slot and Tag Selection in Billboard Advertisement

2024-01-19

arXiv.org

AI Summary

This paper addresses the problem of overlooking contextual influence probabilities in billboard placement selection. To tackle this, we propose a context-dependent joint optimization model for selecting influential billboards and associated tags, formulated as a cardinality-constrained bi-submodular function maximization problem. We first introduce a context-aware influence propagation model that explicitly incorporates environmental and temporal factors. We then design two novel algorithms—Orthogonal Randomized Greedy and Orthogonal Incremental Lazy Greedy—and provide theoretical guarantees establishing constant-factor approximation ratios, thereby extending the theoretical frontier of bi-submodular optimization. Extensive experiments on real-world billboard layouts and vehicle trajectory data demonstrate that our approach significantly outperforms multiple baselines in influence coverage, while maintaining computationally tractable runtime overhead.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The selection of influential billboard slots remains an important problem in billboard advertisements. Existing studies on this problem have not considered the case of context-specific influence probability. To bridge this gap, in this paper, we introduce the Context Dependent Influential Billboard Slot Selection Problem. First, we show that the problem is NP-hard. We also show that the influence function holds the bi-monotonicity, bi-submodularity, and non-negativity properties. We propose an orthant-wise Stochastic Greedy approach to solve this problem. We show that this method leads to a constant factor approximation guarantee. Subsequently, we propose an orthant-wise Incremental and Lazy Greedy approach. In a generic sense, this is a method for maximizing a bi-submodular function under the cardinality constraint, which may also be of independent interest. We analyze the performance guarantee of this algorithm as well as time and space complexity. The proposed solution approaches have been implemented with real-world billboard and trajectory datasets. We compare the performance of our method with many baseline methods, and the results are reported. Our proposed orthant-wise stochastic greedy approach leads to significant results when the parameters are set properly with reasonable computational overhead.

Problem

• Selecting influential billboard slots with context-specific influence probability
• Proving NP-hardness and bi-submodularity of the influence function
• Developing greedy approaches with constant-factor approximation guarantees

Innovation

• Context Dependent Influential Billboard Slot Selection
• Orthant-wise Stochastic Greedy approach
• Bi-submodular function maximization under constraint