eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-07-23
9:1
9:14
10.4230/LIPIcs.CP.2022.9
article
Complexity of Minimum-Size Arc-Inconsistency Explanations
Bessiere, Christian
1
https://orcid.org/0000-0003-4059-6403
Carbonnel, Clément
1
https://orcid.org/0000-0003-2312-2687
Cooper, Martin C.
2
https://orcid.org/0000-0003-4853-053X
Hebrard, Emmanuel
3
https://orcid.org/0000-0003-3131-0709
CNRS, University of Montpellier, France
IRIT, University of Toulouse, France
LAAS CNRS, Toulouse, France
Explaining the outcome of programs has become one of the main concerns in AI research. In constraint programming, a user may want the system to explain why a given variable assignment is not feasible or how it came to the conclusion that the problem does not have any solution. One solution to the latter is to return to the user a sequence of simple reasoning steps that lead to inconsistency. Arc consistency is a well-known form of reasoning that can be understood by a human. We consider explanations as sequences of propagation steps of a constraint on a variable (i.e. the ubiquitous revise function in arc consistency algorithms) that lead to inconsistency. We characterize, on binary CSPs, cases for which providing a shortest such explanation is easy: when domains are Boolean or when variables have maximum degree two. However, these polynomial cases are tight. Providing a shortest explanation is NP-hard if the maximum degree is three, even if the number of variables is bounded, or if domain size is bounded by three. It remains NP-hard on trees, despite the fact that arc consistency is a decision procedure on trees. Finally, the problem is not FPT-approximable unless the Gap-ETH is false.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol235-cp2022/LIPIcs.CP.2022.9/LIPIcs.CP.2022.9.pdf
Constraint programming
constraint propagation
minimum explanations
complexity