Effectiveness of structural restrictions for hybrid CSPs

Vladimir Kolmogorov, Michal Rolínek, Rustem Takhanov

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    3 Citations (Scopus)

    Abstract

    Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism R → Γ between two relational structures, e.g. between two directed graphs. Analyzing its complexity has been a prominent research direction, especially for the fixed template CSPs where the right side Γ is fixed and the left side R is unconstrained. Far fewer results are known for the hybrid setting that restricts both sides simultaneously. It assumes that R belongs to a certain class of relational structures (called a structural restriction in this paper). We study which structural restrictions are effective, i.e. there exists a fixed template Γ (from a certain class of languages) for which the problem is tractable when R is restricted, and NP-hard otherwise. We provide a characterization for structural restrictions that are closed under inverse homomorphisms. The criterion is based on the chromatic number of a relational structure defined in this paper; it generalizes the standard chromatic number of a graph. As our main tool, we use the algebraic machinery developed for fixed template CSPs. To apply it to our case, we introduce a new construction called a “lifted language”. We also give a characterization for structural restrictions corresponding to minor-closed families of graphs, extend results to certain Valued CSPs (namely conservative valued languages), and state implications for (valued) CSPs with ordered variables and for the maximum weight independent set problem on some restricted families of graphs.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    PublisherSpringer Verlag
    Pages566-577
    Number of pages12
    Volume9472
    ISBN (Print)9783662489703
    DOIs
    Publication statusPublished - 2015
    Event26th International Symposium on Algorithms and Computation, ISAAC 2015 - Nagoya, Japan
    Duration: Dec 9 2015Dec 11 2015

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9472
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other26th International Symposium on Algorithms and Computation, ISAAC 2015
    CountryJapan
    CityNagoya
    Period12/9/1512/11/15

    Fingerprint

    Restriction
    Template
    Constraint satisfaction problems
    Directed graphs
    Chromatic number
    Computer science
    Machinery
    Graph in graph theory
    Closed
    Constraint Satisfaction Problem
    Independent Set
    Homomorphisms
    Homomorphism
    Directed Graph
    Minor
    Computer Science
    NP-complete problem
    Generalise
    Computing
    Language

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Kolmogorov, V., Rolínek, M., & Takhanov, R. (2015). Effectiveness of structural restrictions for hybrid CSPs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9472, pp. 566-577). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9472). Springer Verlag. https://doi.org/10.1007/978-3-662-48971-0_48

    Effectiveness of structural restrictions for hybrid CSPs. / Kolmogorov, Vladimir; Rolínek, Michal; Takhanov, Rustem.

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9472 Springer Verlag, 2015. p. 566-577 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9472).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Kolmogorov, V, Rolínek, M & Takhanov, R 2015, Effectiveness of structural restrictions for hybrid CSPs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9472, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9472, Springer Verlag, pp. 566-577, 26th International Symposium on Algorithms and Computation, ISAAC 2015, Nagoya, Japan, 12/9/15. https://doi.org/10.1007/978-3-662-48971-0_48
    Kolmogorov V, Rolínek M, Takhanov R. Effectiveness of structural restrictions for hybrid CSPs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9472. Springer Verlag. 2015. p. 566-577. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-48971-0_48
    Kolmogorov, Vladimir ; Rolínek, Michal ; Takhanov, Rustem. / Effectiveness of structural restrictions for hybrid CSPs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9472 Springer Verlag, 2015. pp. 566-577 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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