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A Complexity Dichotomy for Poset Constraint Satisfaction

Authors Michael Kompatscher, Trung Van Pham

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Michael Kompatscher
Trung Van Pham

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Michael Kompatscher and Trung Van Pham. A Complexity Dichotomy for Poset Constraint Satisfaction. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 47:1-47:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.STACS.2017.47

Abstract

We determine the complexity of all constraint satisfaction problems over partial orders, in particular we show that every such problem is NP-complete or can be solved in polynomial time. This result generalises the complexity dichotomy for temporal constraint satisfaction problems by Bodirsky and Kára. We apply the so called universal-algebraic approach together with tools from model theory and Ramsey theory to prove our result. In the course of this analysis we also establish a structural dichotomy regarding the model theoretic properties of the reducts of the random partial order.
Keywords
  • Constraint Satisfaction
  • Random Partial Order
  • Computational Complexity
  • Universal Algebra
  • Ramsey Theory

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