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Weisfeiler-Leman Invariant Promise Valued CSPs

Authors Libor Barto , Silvia Butti

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Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
Keywords
  • Promise Valued Constraint Satisfaction Problem
  • Linear programming relaxation
  • Distributed algorithms
  • Symmetric fractional polymorphisms
  • Color refinement algorithm

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Abstract

In a recent line of work, Butti and Dalmau have shown that a fixed-template Constraint Satisfaction Problem is solvable by a certain natural linear programming relaxation (equivalent to the basic linear programming relaxation) if and only if it is solvable on a certain distributed network, and this happens if and only if its set of Yes instances is closed under Weisfeiler-Leman equivalence. We generalize this result to the much broader framework of fixed-template Promise Valued Constraint Satisfaction Problems. Moreover, we show that two commonly used linear programming relaxations are no longer equivalent in this broader framework.

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Libor Barto and Silvia Butti. Weisfeiler-Leman Invariant Promise Valued CSPs. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CP.2022.4

Author Details

Libor Barto
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czechia
Silvia Butti
  • Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain

Funding

  • Barto, Libor: Libor Barto has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 771005, CoCoSym).
  • Butti, Silvia: Silvia Butti was supported by a MICCIN grant PID2019-109137GB-C22 and by a fellowship from "la Caixa" Foundation (ID 100010434). The fellowship code is LCF/BQ/DI18/11660056. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 713673.

Acknowledgements

The authors are grateful to Victor Dalmau for his valuable comments.

References

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