Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable

Michael Fellows, Tobias Friedrich, Dan Hermelin, Nina Narodytska, Frances Rosamond

Research output: Contribution to journalConference articlepeer-review

11 Scopus citations


We examine the complexity of constraint satisfaction problems that consist of a set of AllDiff constraints. Such CSPs naturally model a wide range of real-world and combinatorial problems, like scheduling, frequency allocations and graph coloring problems. As this problem is known to be NP-complete, we investigate under which further assumptions it becomes tractable. We observe that a crucial property seems to be the convexity of the variable domains and constraints. Our main contribution is an extensive study of the complexity of Multiple AllDiff CSPs for a set of natural parameters, like maximum domain size and maximum size of the constraint scopes. We show that, depending on the parameter, convexity can make the problem tractable while it is provably intractable in general.

Original languageEnglish
Pages (from-to)522-527
Number of pages6
JournalIJCAI International Joint Conference on Artificial Intelligence
StatePublished - 1 Dec 2011
Externally publishedYes
Event22nd International Joint Conference on Artificial Intelligence, IJCAI 2011 - Barcelona, Catalonia, Spain
Duration: 16 Jul 201122 Jul 2011


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