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Branch-And-Bound Algorithms as Polynomial-Time Approximation Schemes

Authors Koppány István Encz , Monaldo Mastrolilli , Eleonora Vercesi

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ACM Subject Classification
  • Theory of computation → Branch-and-bound
  • Theory of computation → Numeric approximation algorithms
Keywords
  • Branch-and-bound algorithm
  • Polynomial-time approximation scheme
  • Parallel machine scheduling problem
  • Knapsack problem

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Abstract

Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of theoretical knowledge on the B&B framework. Branch-and-bound algorithms typically guarantee that an optimal solution is eventually found. However, we show that the standard implementation of branch-and-bound for certain knapsack and scheduling problems also exhibits PTAS-like behaviour, yielding increasingly better solutions within polynomial time. Our findings are supported by computational experiments and comparisons with benchmark methods.

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Koppány István Encz, Monaldo Mastrolilli, and Eleonora Vercesi. Branch-And-Bound Algorithms as Polynomial-Time Approximation Schemes. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.73

Author Details

Koppány István Encz
  • Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland
  • Istituto Dalle Molle di studi sull'intelligenza artificiale (IDSIA USI-SUPSI), Lugano, Switzerland
Monaldo Mastrolilli
  • Dipartimento Tecnologie innovative, Scuola universitaria professionale della Svizzera italiana, Lugano, Switzerland
  • Istituto Dalle Molle di studi sull'intelligenza artificiale (IDSIA USI-SUPSI), Lugano, Switzerland
Eleonora Vercesi
  • Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland
  • Istituto Dalle Molle di studi sull'intelligenza artificiale (IDSIA USI-SUPSI), Lugano, Switzerland

Funding

The authors were supported by the Swiss National Science Foundation project n. 200021_212929 / 1 "Computational methods for integrality gaps analysis".

Supplementary Materials

References

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