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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

Acknowledgements

We thank the reviewers for their useful comments and suggestions.

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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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