eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-07-23
11:1
11:15
10.4230/LIPIcs.CP.2022.11
article
On Redundancy in Constraint Satisfaction Problems
Carbonnel, Clément
1
https://orcid.org/0000-0003-2312-2687
CNRS, LIRMM, University of Montpellier, France
A constraint language Γ has non-redundancy f(n) if every instance of CSP(Γ) with n variables contains at most f(n) non-redundant constraints. If Γ has maximum arity r then it has non-redundancy O(n^r), but there are notable examples for which this upper bound is far from the best possible. In general, the non-redundancy of constraint languages is poorly understood and little is known beyond the trivial bounds Ω(n) and O(n^r).
In this paper, we introduce an elementary algebraic framework dedicated to the analysis of the non-redundancy of constraint languages. This framework relates redundancy-preserving reductions between constraint languages to closure operators known as pattern partial polymorphisms, which can be interpreted as generic mechanisms to generate redundant constraints in CSP instances. We illustrate the power of this framework by deriving a simple characterisation of all languages of arity r having non-redundancy Θ(n^r).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol235-cp2022/LIPIcs.CP.2022.11/LIPIcs.CP.2022.11.pdf
Constraint satisfaction problem
redundancy
universal algebra
extremal combinatorics