Minimizing Regret in Billboard Advertisement under Zonal Influence Constraint

TL;DR

The paper tackles regret minimization for billboard slot allocation under a zonal influence constraint, a problem that is NP-hard under disjoint-slot allocations. It introduces four heuristic approaches—Budget-Effective Greedy (BG), Randomized Budget-Effective Greedy (RG), Randomized Synchronous Greedy (RSG), and Randomized Advertiser Exchange (RAE)—to balance satisfaction across zones while minimizing total regret, which combines unsatisfied and excessive components. The regret model accounts for payments, demand coverage, and a penalty parameter, and the authors analyze time/space complexity alongside extensive experiments on NYC/LA trajectory data and Lamar billboards. Results show that RSG and RAE often outperform baselines and the simpler BG/RG, offering practical, scalable strategies for providers to allocate slots under zonal constraints and varying demand regimes. The work provides a foundation for further exploration of local-search enhancements to increasingly improve regret minimization in real-world, zonal billboard networks.

Abstract

In a typical billboard advertisement technique, a number of digital billboards are owned by an influence provider, and many advertisers approach the influence provider for a specific number of views of their advertisement content on a payment basis. If the influence provider provides the demanded or more influence, then he will receive the full payment or else a partial payment. In the context of an influence provider, if he provides more or less than an advertiser's demanded influence, it is a loss for him. This is formalized as 'Regret', and naturally, in the context of the influence provider, the goal will be to allocate the billboard slots among the advertisers such that the total regret is minimized. In this paper, we study this problem as a discrete optimization problem and propose four solution approaches. The first one selects the billboard slots from the available ones in an incremental greedy manner, and we call this method the Budget Effective Greedy approach. In the second one, we introduce randomness with the first one, where we perform the marginal gain computation for a sample of randomly chosen billboard slots. The remaining two approaches are further improvements over the second one. We analyze all the algorithms to understand their time and space complexity. We implement them with real-life trajectory and billboard datasets and conduct a number of experiments. It has been observed that the randomized budget effective greedy approach takes reasonable computational time while minimizing the regret.

Figures (9)

• Figure 1: Schematic Diagram
• Figure 2: Regret varying $\delta$, when $\lambda = 1\%, \mathcal{|A|} = 100$$(a, b, c, d, e)$, when $\lambda = 2\%, \mathcal{|A|} = 50$$(f, g, h, i, j),$ when $\lambda = 5\%, \mathcal{|A|} = 20$$(k,\ell,m, n,o)$, when $\lambda = 10\%, \mathcal{|A|} = 10$$(p, q, r, s, t)$, when $\lambda = 20\%, \mathcal{|A|} = 5$$(u, v, w, x, y),$ for NYC dataset
• Figure 3: Regret varying $\delta$, when $\lambda = 1\%, \mathcal{|A|} = 100$$(a, b, c, d, e)$, when $\lambda = 2\%, \mathcal{|A|} = 50$$(f, g, h, i, j),$ when $\lambda = 5\%, \mathcal{|A|} = 20$$(k,l,m, n,o)$, when $\lambda = 10\%, \mathcal{|A|} = 10$$(p, q, r, s, t)$, when $\lambda = 20\%, \mathcal{|A|} = 5$$(u, v, w, x, y),$ for LA dataset
• Figure 4: Efficiency Study on NYC
• Figure 5: Efficiency Study on LA

Theorems & Definitions (8)

• Definition 1: Influence of Billboard Slots
• Definition 2: Zonal Influence Constraint
• Definition 3: The Regret Model
• Definition 4: Feasible Allocation
• Definition 5: Total Regret Associated with an Allocation
• Definition 6: Regret Minimization with Zonal Influence Constraint
• Theorem 1
• Definition 7: Budget Effective Advertiser