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Influential Billboard Slot Selection under Zonal Influence Constraint

Dildar Ali, Suman Banerjee, Yamuna Prasad

TL;DR

This work tackles the problem of Influential Billboard Slot Selection under Zonal Influence Constraint (IBSSP), formulating it as maximizing $\mathcal{I}(\mathcal{S})$ under a budget and zone-specific influence demands. It introduces two solution approaches: a simple greedy allocation and a Branch-and-Bound framework with fast and bound-estimation techniques, along with formal complexity and performance analyses. Empirical evaluation on NYC and LA datasets shows that the Branch-and-Bound method (BBS) delivers higher influence than baselines, albeit with higher runtime, while the greedy approach provides a scalable, though sometimes less optimal, alternative. The results demonstrate the practical value of incorporating zonal constraints in billboard slot selection and highlight the trade-offs between solution quality and computational cost, suggesting directions for more scalable bound-based methods in future work.

Abstract

Given billboard and trajectory database, finding a limited number of billboard slots for maximizing the influence is an important problem in the context of billboard advertisement. Most of the existing literature focused on the influential slot selection problem without considering any specific zonal influence constraint. To bridge this gap in this paper, we introduce and study the Influential Billboard Slot Selection Problem Under Zonal Influence Constraint. We propose a simple greedy approach to solve this problem. Though this method is easy to understand and simple to implement due to the excessive number of marginal gain computations, this method is not scalable. We design a branch and bound framework with two bound estimation techniques that divide the problem into different zones and integrate the zone-specific solutions to obtain a solution for the whole. We implement both the solution methodologies with real-world billboard and trajectory datasets and several experiments have been reported. We compare the performance of the proposed solution approaches with several baseline methods. The results show that the proposed approaches lead to more effective solutions with reasonable computational overhead than the baseline methods.

Influential Billboard Slot Selection under Zonal Influence Constraint

TL;DR

This work tackles the problem of Influential Billboard Slot Selection under Zonal Influence Constraint (IBSSP), formulating it as maximizing under a budget and zone-specific influence demands. It introduces two solution approaches: a simple greedy allocation and a Branch-and-Bound framework with fast and bound-estimation techniques, along with formal complexity and performance analyses. Empirical evaluation on NYC and LA datasets shows that the Branch-and-Bound method (BBS) delivers higher influence than baselines, albeit with higher runtime, while the greedy approach provides a scalable, though sometimes less optimal, alternative. The results demonstrate the practical value of incorporating zonal constraints in billboard slot selection and highlight the trade-offs between solution quality and computational cost, suggesting directions for more scalable bound-based methods in future work.

Abstract

Given billboard and trajectory database, finding a limited number of billboard slots for maximizing the influence is an important problem in the context of billboard advertisement. Most of the existing literature focused on the influential slot selection problem without considering any specific zonal influence constraint. To bridge this gap in this paper, we introduce and study the Influential Billboard Slot Selection Problem Under Zonal Influence Constraint. We propose a simple greedy approach to solve this problem. Though this method is easy to understand and simple to implement due to the excessive number of marginal gain computations, this method is not scalable. We design a branch and bound framework with two bound estimation techniques that divide the problem into different zones and integrate the zone-specific solutions to obtain a solution for the whole. We implement both the solution methodologies with real-world billboard and trajectory datasets and several experiments have been reported. We compare the performance of the proposed solution approaches with several baseline methods. The results show that the proposed approaches lead to more effective solutions with reasonable computational overhead than the baseline methods.
Paper Structure (35 sections, 2 theorems, 2 equations, 3 figures, 1 table, 4 algorithms)

This paper contains 35 sections, 2 theorems, 2 equations, 3 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background.
  3. Motivation.
  4. Our Contributions.
  5. Organization of the Paper.
  6. Background and Problem Definition
  7. Proposed Solution Approach
  8. Simple Greedy Allocation Scheme.
  9. Complexity Analysis.
  10. Branch and Bound Approach.
  11. Complexity Analysis.
  12. Fast Bound Estimation.
  13. Complexity Analysis.
  14. Bound Estimation.
  15. Complexity Analysis.
  16. ...and 20 more sections

Key Result

theorem thmcountertheorem

The Influential Billboard Slot Selection Problem Under Zonal Influence Constraint is NP-hard and hard to approximate with a constant factor algorithm.

Figures (3)

  • Figure 1: Billboard Info.
  • Figure 2: A running example
  • Figure 3: Varying Budget in NYC (a,b), LA (c,d), Varying $\theta$ in NYC (e,f), Varying No. of Slot in NYC (g), Varying $\epsilon$ in NYC (h,i)

Theorems & Definitions (5)

  • definition thmcounterdefinition: Billboard Slot
  • definition thmcounterdefinition: Influence of Billboard Slots
  • definition thmcounterdefinition: Zonal Influence Constraint
  • theorem thmcountertheorem
  • theorem thmcountertheorem