Skip to main content

Research Repository

Advanced Search

Complexity of clausal constraints over chains

Creignou, N.; Hermann, M.; Krokhin, A.; Salzer, G.


N. Creignou

M. Hermann

G. Salzer


We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x≥d and x≤d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NP-complete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature.


Creignou, N., Hermann, M., Krokhin, A., & Salzer, G. (2008). Complexity of clausal constraints over chains. Theory of Computing Systems, 42(2), 239-255.

Journal Article Type Article
Publication Date Feb 1, 2008
Deposit Date Dec 15, 2009
Journal Theory of Computing Systems
Print ISSN 1432-4350
Electronic ISSN 1433-0490
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 42
Issue 2
Pages 239-255
Keywords Constraint satisfaction problems, Complexity, Finite totally ordered domains, Inequalities, Clausal patterns, Dichotomy theorem.
Publisher URL