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Revisiting Integer Programming Encodings of Acyclicity

Authors Masood Feyzbakhsh Rankooh , Matti Järvisalo

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LIPIcs.CP.2026.47.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Integer programming
Keywords
  • Operations research
  • integer programming encodings
  • acyclicity
  • tightness

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Abstract

We study generic integer programming (IP) encodings of acyclicity in directed graphs as a key constraint in various real-world problem domains. We analyze both classical and more recently-proposed generic acyclicity encodings, including Miller-Tucker-Zemlin (MTZ), feedback vertex set (FVS), vertex elimination (VE), and cycle elimination (CE) based encodings in terms of their linear programming (LP) relaxation tightness. We also introduce hybrid encodings combining sought-after properties of the individual encodings. For the hybrids, we establish tightness guarantees for their LP relaxations that interpolate smoothly between the individual encodings. Our results show that VE and CE yield equally strong relaxations and strictly dominate MTZ and FVS, while the hybrid encoding schemes become increasingly tight as the elimination prefix grows. Mapping theory to practice, we empirically evaluate the encodings on both direct IP encodings of problem domains, where acyclicity is a key constraint. The results both validate our theoretical findings and yield promising runtime performance.

Cite As Get BibTex

Masood Feyzbakhsh Rankooh and Matti Järvisalo. Revisiting Integer Programming Encodings of Acyclicity. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 47:1-47:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.47

Author Details

Masood Feyzbakhsh Rankooh
  • HIIT, Department of Computer Science, University of Helsinki, Finland
Matti Järvisalo
  • HIIT, Department of Computer Science, University of Helsinki, Finland

Funding

  • Rankooh, Masood Feyzbakhsh: Financially supported by Helsinki Institute for Information Technology HIIT.
  • Järvisalo, Matti: Financially supported by Research Council of Finland under grant 356046.

Acknowledgements

The authors wish to thank the Finnish Computing Competence Infrastructure (FCCI) for supporting this project with computational and data storage resources.

Supplementary Materials

References

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