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DOI: 10.4230/LIPIcs.STACS.2017.47

A Complexity Dichotomy for Poset Constraint Satisfaction

Authors: Michael Kompatscher and Trung Van Pham

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

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.

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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)

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@InProceedings{kompatscher_et_al:LIPIcs.STACS.2017.47,
  author =	{Kompatscher, Michael and Pham, Trung Van},
  title =	{{A Complexity Dichotomy for Poset Constraint Satisfaction}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{47:1--47:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.47},
  URN =		{urn:nbn:de:0030-drops-69850},
  doi =		{10.4230/LIPIcs.STACS.2017.47},
  annote =	{Keywords: Constraint Satisfaction, Random Partial Order, Computational Complexity, Universal Algebra, Ramsey Theory}
}

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A Complexity Dichotomy for Poset Constraint Satisfaction

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