QCSP on Reflexive Tournaments

Benoit Larose; Petar Markovic; Barnaby Martin; Daniel Paulusma; Siani Smith; Stanislav Zivny

doi:10.1145/3508069

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arXiv · 2104.10570

QCSP on Reflexive Tournaments

Benoit Larose·Petar Markovic·Barnaby Martin·Daniel Paulusma·Siani Smith·Stanislav Zivny

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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 H_1,...,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.

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BibTeX RIS

Benoit Larose, Petar Markovic, Barnaby Martin, Daniel Paulusma, Siani Smith, Stanislav Zivny. 2021-04-21. QCSP on Reflexive Tournaments. https://doi.org/10.1145/3508069

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