Weisfeiler-Leman Invariant Promise Valued CSPs

Authors Libor Barto , Silvia Butti



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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

Acknowledgements

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

Cite AsGet BibTex

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

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.

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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