eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-23
28:1
28:17
10.4230/LIPIcs.MFCS.2024.28
article
Generalized Completion Problems with Forbidden Tournaments
Bitter, Zeno
1
https://orcid.org/0009-0004-7965-6965
Mottet, Antoine
1
https://orcid.org/0000-0002-3517-1745
Hamburg University of Technology, Research Group for Theoretical Computer Science, Germany
A recent result by Bodirsky and Guzmán-Pro gives a complexity dichotomy for the following class of computational problems, parametrized by a finite family F of finite tournaments: given an undirected graph, does there exist an orientation of the graph that avoids every tournament in F? One can see the edges of the input graphs as constraints imposing to find an orientation. In this paper, we consider a more general version of this problem where the constraints in the input are not necessarily about pairs of variables and impose local constraints on the global oriented graph to be found. Our main result is a complexity dichotomy for such problems, as well as a classification of such problems where the yes-instances have bounded treewidth duality. As a consequence, we obtain a streamlined proof of the result by Bodirsky and Guzmán-Pro using the theory of smooth approximations due to Mottet and Pinsker.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol306-mfcs2024/LIPIcs.MFCS.2024.28/LIPIcs.MFCS.2024.28.pdf
Tournaments
completion problems
constraint satisfaction problems
homogeneous structures
polymorphisms