eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-29
15:1
15:17
10.4230/LIPIcs.CP.2024.15
article
CSPs with Few Alien Constraints
Jonsson, Peter
1
Lagerkvist, Victor
1
Osipov, George
1
Department of Computer and Information Science, Linköping University, Sweden
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure 𝒜 is satisfiable (CSP(𝒜)). We consider CSP(𝒜 ∪ ℬ) where 𝒜 is a structure and ℬ is an alien structure, and analyse its (parameterized) complexity when at most k alien constraints are allowed. We establish connections and obtain transferable complexity results to several well-studied problems that previously escaped classification attempts. Our novel approach, utilizing logical and algebraic methods, yields an FPT versus pNP dichotomy for arbitrary finite structures and sharper dichotomies for Boolean structures and first-order reducts of (ℕ, =) (equality CSPs), together with many partial results for general ω-categorical structures.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol307-cp2024/LIPIcs.CP.2024.15/LIPIcs.CP.2024.15.pdf
Constraint satisfaction
parameterized complexity
hybrid theories