Multi-product Influence Maximization in Billboard Advertisement

TL;DR

This work tackles the problem of maximizing influence from multiple products via billboard slots under a shared budget. It introduces two problem variants—Common Slot Selection and Disjoint Slot Selection—and casts them as multi-submodular cover problems, proposing a continuous greedy bi-criteria algorithm for the common case and a sampling-based approach for the disjoint case, with Hoeffding-based guarantees. The paper provides theoretical modeling of influence via trajectory data, submodular extensions, and generalized cover formulations, along with extensive experiments on NYC and LA datasets demonstrating effectiveness and scalability. The results show the proposed methods can achieve higher multi-product influence under budget constraints compared to baselines, validating the practical value for advertisers and billboard networks in real-world settings.

Abstract

Billboard Advertisement has emerged as an effective out-of-home advertisement technique where the goal is to select a limited number of slots and play advertisement content over there with the hope that this will be observed by many people, and effectively, a significant number of them will be influenced towards the brand. Given a trajectory and a billboard database and a positive integer $k$, how can we select $k$ highly influential slots to maximize influence? In this paper, we study a variant of this problem where a commercial house wants to make a promotion of multiple products, and there is an influence demand for each product. We have studied two variants of the problem. In the first variant, our goal is to select $k$ slots such that the respective influence demand of each product is satisfied. In the other variant of the problem, we are given with $\ell$ integers $k_1,k_2, \ldots, k_{\ell}$, the goal here is to search for $\ell$ many set of slots $S_1, S_2, \ldots, S_{\ell}$ such that for all $i \in [\ell]$, $|S_{i}| \leq k_i$ and for all $i \neq j$, $S_i \cap S_j=\emptyset$ and the influence demand of each of the products gets satisfied. We model the first variant of the problem as a multi-submodular cover problem and the second variant as its generalization. For solving the first variant, we adopt the bi-criteria approximation algorithm, and for the other variant, we propose a sampling-based approximation algorithm. Extensive experiments with real-world trajectory and billboard datasets highlight the effectiveness and efficiency of the proposed solution approach.

Figures (5)

• Figure 1: Continuous Greedy Algorithm
• Figure 2: Bi-criteria Approximation Algorithm for Multi-Product Influence Maximization
• Figure 3: Randomized Algorithm for Multi-Product Influence Maximization
• Figure 4: Plots for NYC dataset: $(a,b)$$\alpha$ vs. Influence, $(c,d)$$\alpha$ vs. No. of Slots, $(e,f)$$\alpha$ vs. Time, and $(g,h)$$\alpha$ vs. Cost
• Figure 5: Plots for LA dataset: $(a,b)$$\alpha$ vs. Influence, $(c,d)$$\alpha$ vs. No. of Slots, $(e,f)$$\alpha$ vs. Time, and $(g,h)$$\alpha$ vs. Cost

Theorems & Definitions (11)

• definition 1: Billboard Slot
• definition 2: Influence Probability of a Billboard slot
• definition 3: Influence of Billboard Slots
• definition 4: Product Specific Influence
• theorem 1
• theorem 2
• theorem 3
• theorem 4
• proposition 1
• theorem 5