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DOI: 10.4230/LIPIcs.ESA.2021.58
QCSP on Reflexive Tournaments

Authors: Benoît Larose, Petar Marković, Barnaby Martin, Daniël Paulusma, Siani Smith, and Stanislav Živný

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components H₁,…,H_n so that there exists an edge from every vertex of H_i to every vertex of H_j if and only if i < j. We prove that if H has both its initial and final strongly connected component (possibly equal) of size 1, then QCSP(H) is in NL and otherwise QCSP(H) is NP-hard.
Cite as

Benoît Larose, Petar Marković, Barnaby Martin, Daniël Paulusma, Siani Smith, and Stanislav Živný. QCSP on Reflexive Tournaments. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{larose_et_al:LIPIcs.ESA.2021.58,
  author =	{Larose, Beno\^{i}t and Markovi\'{c}, Petar and Martin, Barnaby and Paulusma, Dani\"{e}l and Smith, Siani and \v{Z}ivn\'{y}, Stanislav},
  title =	{{QCSP on Reflexive Tournaments}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.58},
  URN =		{urn:nbn:de:0030-drops-146392},
  doi =		{10.4230/LIPIcs.ESA.2021.58},
  annote =	{Keywords: computational complexity, algorithmic graph theory, quantified constraints, universal algebra, constraint satisfaction}
}
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