Constraint satisfaction problems: Convexity makes All Different constraints tractable

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

    Research output: Contribution to journalArticlepeer-review


    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 even though it is provably intractable in general. Interestingly, the convexity of constraints is the key property in achieving fixed parameter tractability, while the convexity of domains does not usually make the problem easier.

    Original languageEnglish
    Pages (from-to)81-89
    Number of pages9
    JournalTheoretical Computer Science
    Publication statusPublished - 11 Feb 2013


    Dive into the research topics of 'Constraint satisfaction problems: Convexity makes All Different constraints tractable'. Together they form a unique fingerprint.

    Cite this