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The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains

Authors Caterina Viola , Stanislav Živný

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Author Details

Caterina Viola
  • Department of Computer Science, University of Oxford, UK
Stanislav Živný
  • Department of Computer Science, University of Oxford, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper reflects only the authors' views and not the views of the ERC or the European Commission. The European Union is not liable for any use that may be made of the information contained therein.
  • Živný, Stanislav: Royal Society University Research Fellowship.

Acknowledgements

We thank the reviewers for their useful comments and suggestions.

Cite AsGet BibTex

Caterina Viola and Stanislav Živný. The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 85:1-85:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.MFCS.2020.85

Abstract

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami [SODA'20] for promise (non-valued) CSPs (on finite domains).

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Constraint and logic programming
Keywords
  • promise constraint satisfaction
  • valued constraint satisfaction
  • convex relaxations
  • polymorphisms

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