LIPIcs.CP.2024.35.pdf
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On the Complexity of Integer Programming with Fixed-Coefficient Scaling (Short Paper)
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30th International Conference on Principles and Practice of Constraint Programming (CP 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Principles and Practice of Constraint Programming (CP) - License:
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- Publication Date: 2024-08-29
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Acknowledgements
I wish to thank P. Jonsson and G. Osipov for discussions and feedback.
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Jorke M. de Vlas. On the Complexity of Integer Programming with Fixed-Coefficient Scaling (Short Paper). In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 35:1-35:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.35
Abstract
We give a polynomial time algorithm that solves a CSP over 𝐙 with linear inequalities of the form c^{a₁} x - c^{a₂} y ≤ b where x and y are variables, a₁, a₂ and b are parameters, and c is a fixed constant. This is a step in classifying the complexity of CSP(Γ) for first-order reducts Γ from (𝐙, < ,+,1). The algorithm works by first reducing the infinite domain to a finite domain by inferring an upper bound on the size of the smallest solution, then repeatedly merging consecutive constraints into new constraints, and finally solving the problem using arc consistency.
Subject Classification
ACM Subject Classification
- Theory of computation → Design and analysis of algorithms
- Theory of computation → Complexity theory and logic
Keywords
- constraint satisfaction problems
- integer programming
- CSP dichotomy
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