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Improved Approximation Guarantees for Advertisement Placement

Authors Waldo Gálvez , Roberto Oliva, Victor Verdugo

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Advertisement Placement
  • Two-dimensional Packing
  • Geometric Knapsack
  • Resource Allocation

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Abstract

The advertisement placement problem involves selecting and scheduling ads within a timeline that has capacity constraints to maximize profit. Each task is characterized by its height, width, and profit, and must be fully scheduled across multiple time slots. This problem models practical scenarios such as internet advertising and energy management, and it also generalizes classical combinatorial optimization problems like the knapsack and bin packing problems.
We present a simple (2+ε)-approximation algorithm for any ε > 0, which improves upon the state-of-the-art 3+ε factor established by Freund and Naor twenty years ago. Our approach combines rounding techniques with dynamic programming and an efficient extension of list scheduling. Furthermore, we enhance this method with linear programming techniques to provide an almost optimal (1+ε)-approximation algorithm under resource augmentation, which allows for a slight increase in time slot capacities.

Cite As Get BibTex

Waldo Gálvez, Roberto Oliva, and Victor Verdugo. Improved Approximation Guarantees for Advertisement Placement. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.10

Author Details

Waldo Gálvez
  • Department of Computer Science, Universidad de Concepción, Chile
Roberto Oliva
  • Institute of Engineering Sciences, Universidad de O'Higgins, Rancagua, Chile
Victor Verdugo
  • Institute for Mathematical and Computational Engineering, Department of Industrial and Systems Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

Funding

  • Gálvez, Waldo: Supported by ANID through grants SIA85220118 and Fondecyt de Iniciación 11230663.
  • Verdugo, Victor: Supported by ANID through grant Fondecyt 1241846.

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