Trajectory-Driven Multi-Product Influence Maximization in Billboard Advertising

TL;DR

This work tackles trajectory-driven, multi-product influence maximization for billboard advertising under budget constraints, introducing two variants: a common-slot problem where all products share the same slot set, and a disjoint-slot problem with per-product slot budgets. It models these as multi-submodular cover problems and develops distinct algorithms: a continuous-greedy bi-criteria approach with randomized rounding for the common-slot case, and a sampling-based randomized method plus a greedy primal–dual algorithm for the disjoint-slot case, all backed by theoretical guarantees. The authors validate their methods on real NYC and LA trajectory-billboard data, showing that PDG often achieves higher influence satisfaction and better budget utilization, while BCA provides high influence at higher cost, and the baselines struggle under higher demand. The results demonstrate scalable, effective allocation of billboard slots to multiple products, offering practical guidance for influence providers and advertisers in dynamic urban environments.

Abstract

Billboard Advertising has emerged as an effective out-of-home advertising technique, where the goal is to select a limited number of slots and play advertisement content there, with the hope that it 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. To solve the common-slot variant, we formulate the problem as a multi-submodular cover problem and design a bi-criteria approximation algorithm based on the continuous greedy framework and randomized rounding. For the disjoint-slot variant, we proposed a sampling-based approximation approach along with an efficient primal-dual greedy algorithm that enforces disjointness naturally. Extensive experiments with real-world trajectory and billboard datasets highlight the effectiveness and efficiency of the proposed solution approaches.

Figures (4)

• Figure 1: Schematic Diagram of the Product to Slot Allocation
• Figure 2: A motivating example
• Figure 3: Varying $\beta$ and $|\mathcal{P}|$ value $\alpha$ vs. Influence $(a,b,c,d,e)$, $\alpha$ vs. Cost $(f,g,h,i,j)$. $\alpha$ vs. No. of Slots $(k,\ell,m,n,o)$, $\alpha$ vs. Time, and $(p,q,r,s,t)$ for LA Dataset
• Figure 4: Varying $\beta$ and $|\mathcal{P}|$ value $\alpha$ vs. Influence $(a,b,c,d,e)$, $\alpha$ vs. Cost $(f,g,h,i,j)$. $\alpha$ vs. No. of Slots $(k,\ell,m,n,o)$, $\alpha$ vs. Time, and $(p,q,r,s,t)$ for NYC Dataset

Theorems & Definitions (18)

• Definition 1: Billboard Slot
• Definition 2: Influence Probability of a Billboard slot
• Definition 3: Influence of Billboard Slots
• Definition 4: Product Specific Influence
• Example 1
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Proposition 5