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QCSP on reflexive tournaments

Larose, B. and Markovic, P. and Martin, B. and Paulusma, D. and Smith, S. and Zivny, S. (2021) 'QCSP on reflexive tournaments.', The 29th Annual European Symposium on Algorithms (ESA 2021) Lisbon / Online, 6-8 Sept 2021.


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, . . . , Hn so that there exists an edge from every vertex of Hi to every vertex of Hj 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.

Item Type:Conference item (Paper)
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution 4.0.
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Publisher statement:© Benoît Larose, Peter Marković, Barnaby Martin, Daniël Paulusma, Siani Smith and Stanislav Živný; licensed under Creative Commons License CC-BY 4.0 29th Annual European Symposium on Algorithms (ESA 2021). Editors: Petra Mutzel, Rasmus Pagh, and Grzegorz Herman; Article No. 2; pp. 2:1–2:15 Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany
Date accepted:23 June 2021
Date deposited:25 August 2021
Date of first online publication:2021
Date first made open access:09 September 2021

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