Balanced Popularity in Multi-Product Billboard Advertisement

TL;DR

The paper tackles selecting billboard slots to promote multiple products under budget and fairness constraints, aiming to maximize the total influence across products. It formulates the Multi‑Product Influence Maximization for Balanced Popularity (MPIM) problem and develops three approaches: a linear programming (LP) relaxation with randomized rounding (RR) and a balance‑correction step, plus a Greedy Heuristic with Balance Correction. The authors prove NP‑hardness and provide complexity analyses, then validate their methods on real trajectory and billboard datasets from NYC and LA, showing that LP+RR achieves higher aggregated influence with tighter balance than baselines, while the greedy method offers faster, scalable performance. The work enables more effective and fair multi‑product billboard campaigns by balancing cross‑product influence while respecting slot budgets, with practical implications for advertisers and outdoor advertising platforms.

Abstract

The billboard advertisement has emerged as an effective out-of-home advertisement technique where the objective is to choose a limited number of slots to play some advertisement content (e.g., animation, video, etc.) with the hope that the content will be visible to a large number of travelers, and this will be helpful to earn more revenue. In this paper, we study a variant of the influential slot selection problem where the advertiser wants to promote multiple products. Formally, we call this problem the \textsc{Multi-Product Influence Maximization Problem for the Balanced Popularity} Problem. The input to our problem is a trajectory and a billboard database, as well as a budget for each product. The goal here is to choose a subset of slots for each product such that the aggregated influence of all the products gets maximized subject to the following two constraints: total selection cost for each product is less than or equal to the allocated budget for that product, and the difference between the influence for any two products is less than or equal to a given threshold. We show that the problem is NP-hard to solve optimally. We formulate this problem as a linear programming problem and use linear programming relaxation with randomized rounding. Further, we propose a greedy-based heuristic with balance correction to solve this problem. We conduct a number of experiments with real-world trajectory and billboard datasets, and the results are reported. From the reported results, we observe that the proposed solution approaches lead to more influence compared to many baseline methods.

Figures (2)

• Figure 1: Algorithms Vs. Influence $(a,b,c,d)$, Varying $\alpha$ Vs. Fairness Gap (e), Time (f), Varying $\epsilon$ Vs. Influence (g), Varying $\theta$ Vs. Fairness Gap (h) with $|\mathcal{P}| = 20$, $\beta = 5\%$ for NYC dataset
• Figure 2: Algorithms Vs. Influence $(a,b,c,d)$, Varying $\alpha$ Vs. Fairness Gap (e), Time (f), Varying $\epsilon$ Vs. Influence (g), Varying $\theta$ Vs. Fairness Gap (h) with $|\mathcal{P}| = 20$, $\beta = 5\%$ for LA dataset

Theorems & Definitions (7)

• definition thmcounterdefinition: Billboard Slot
• definition thmcounterdefinition: Influence Probability of a Billboard slot
• definition thmcounterdefinition: Influence of Billboard Slots
• definition thmcounterdefinition: Product Specific Influence
• theorem thmcountertheorem
• theorem thmcountertheorem
• theorem thmcountertheorem