eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
58:1
58:15
10.4230/LIPIcs.ESA.2021.58
article
QCSP on Reflexive Tournaments
Larose, Benoît
1
Marković, Petar
2
Martin, Barnaby
3
Paulusma, Daniël
3
Smith, Siani
3
Živný, Stanislav
4
LACIM, University of Québec, Montréal, Canada
Department of Mathematics and Informatics, University of Novi Sad, Serbia
Department of Computer Science, Durham University, UK
Department of Computer Science, University of Oxford, UK
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.58/LIPIcs.ESA.2021.58.pdf
computational complexity
algorithmic graph theory
quantified constraints
universal algebra
constraint satisfaction