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 publicationAlgorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings
EditorsKhaled Elbassioni, Kazuhisa Makino
PublisherSpringer Verlag
Pages566-577
Number of pages12
ISBN (Print)9783662489703
DOIs
Publication statusPublished - Jan 1 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

    Fingerprint

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kolmogorov, V., Rolínek, M., & Takhanov, R. (2015). Effectiveness of structural restrictions for hybrid CSPs. In K. Elbassioni, & K. Makino (Eds.), Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings (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