Skip to main content
SpringerLink
Log in

The Broken-Triangle Property with Adjoint Values

  • Conference paper
  • First Online:
Frontiers in Algorithmics (FAW 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10336))

Included in the following conference series:

  • 557 Accesses

Abstract

Recently, the Broken Triangle Property (BTP) and its extensions have been proposed to identify hybrid tractable classes of Constraint Satisfaction Problems (CSPs). In this paper, we extend the BTP to the concept of the Broken Triangle Property with adjoint values (BTPv), and then identify a more general hybrid tractable class of binary CSPs. To prove tractability, we present a polynomial-time algorithm to solve CSP instances in the new tractable class using a novel variable selection mechanism, and show correctness of it. We also show that determining whether an instance is in the class can be achieved efficiently. Furthermore, we provide comparisons with the BTP and its extensions showing that as a generalization of the BTP, the BTPv can find novel tractable CSPs, which cannot be identified by those existing tractable classes.

This work was supported by the National Natural Science Foundation of China (No. 61402070, No. 61370156, No. 61503074, No. 61672122 and No. 61602077), and Natural Science Foundation of Liaoning Province (No. 2015020023).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dechter, R.: Constraint Processing. Morgan Kaufmann, Burlington (2003)

    MATH  Google Scholar 

  2. Carbonnel, C., Cooper, M.C.: Tractability in constraint satisfaction problems: a survey. Constraints 21(2), 115–144 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cooper, M.C., Jeavons, P.G., Salamon, A.Z.: Generalizing constraint satisfaction on trees: hybrid tractability and variable elimination. Artif. Intell. 174(9–10), 570–584 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohen, D.A., Cooper, M.C., Creed, P., Marx, D., Salamon, A.Z.: The tractability of CSP classes defined by forbidden patterns. J. Artif. Intell. Res. (JAIR) 45, 47–78 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Cohen, D.A., Cooper, M.C., Jeavons, P.G., Zivny, S.: Tractable classes of binary CSPs defined by excluded topological minors. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 1945–1951 (2015)

    Google Scholar 

  6. Thorstensen, E.: Hybrid tractability of constraint satisfaction problems with global constraints. Ph.D. thesis, University of Oxford (2013)

    Google Scholar 

  7. Cooper, M.C., Duchein, A., Mouelhi, A.E., Escamocher, G., Terrioux, C., Zanuttini, B.: Broken triangles: from value merging to a tractable class of general-arity constraint satisfaction problems. Artif. Intell. 234, 196–218 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cooper, M.C., Jeavons, P.G., Salamon, A.Z.: Hybrid tractable CSPs which generalize tree structure. In: Proceedings of the ECAI 2008, pp. 530–534. IOS Press (2008)

    Google Scholar 

  9. Cohen, D.A., Cooper, M.C., Escamocher, G., Zivny, S.: Variable elimination in binary CSP via forbidden patterns. In: Rossi, F. (ed.) Proceedings of the IJCAI, IJCAI 2013. AAAI, Menlo Park (2013)

    Google Scholar 

  10. Mouelhi, A.E., Jégou, P., Terrioux, C., Classes, H.T.: From theory to practice. In: Proceedings of the ICTAI 2014, pp. 437–445 (2014)

    Google Scholar 

  11. Cooper, M.C., Zivny, S.: Hybrid tractability of valued constraint problems. Artif. Intell. 175(9–10), 1555–1569 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gao, J., Yin, M., Zhou, J.: Hybrid tractable classes of binary quantified constraint satisfaction problems. In: Burgard, W., Roth, D. (eds.) Proceedings of the AAAI 2011. AAAI Press (2011)

    Google Scholar 

  13. Jégou, P., Terrioux, C.: The extendable-triple property: a new CSP tractable class beyond BTP. In: Proceedings of the AAAI 2015 (2015)

    Google Scholar 

  14. Mouelhi, A.E., Jégou, P., Terrioux, C.: A hybrid tractable class for non-binary CSPs. In: Proceedings of the ICTAI 2013, pp. 947–954. IEEE Computer Society (2013)

    Google Scholar 

  15. Naanaa, W.: Unifying and extending hybrid tractable classes of CSPs. J. Exp. Theor. Artif. Intell. 25(4), 407–424 (2013)

    Article  Google Scholar 

  16. Bessière, C., Régin, J.: Refining the basic constraint propagation algorithm. In: Nebel, B. (ed.) Proceedings of the IJCAI 2001, pp. 309–315. Morgan Kaufmann (2001)

    Google Scholar 

  17. Singh, M.: Path consistency revisited. Int. J. Artif. Intell. Tools 5(1–2), 127–142 (1996)

    Article  Google Scholar 

  18. Green, M.J., Cohen, D.A.: Domain permutation reduction for constraint satisfaction problems. Artif. Intell. 172(8–9), 1094–1118 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Jeavons, P., Cooper, M.C.: Tractable constraints on ordered domains. Artif. Intell. 79(2), 327–339 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Jian Gao, Rong Chen & Hui Li

  2. College of Computer Science, Northeast Normal University, Changchun, 130024, China

    Minghao Yin

Authors
  1. Jian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Minghao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jian Gao , Rong Chen , Minghao Yin or Hui Li .

Editor information

Editors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Mingyu Xiao

  2. University of Bergen, Bergen, Norway

    Frances Rosamond

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gao, J., Chen, R., Yin, M., Li, H. (2017). The Broken-Triangle Property with Adjoint Values. In: Xiao, M., Rosamond, F. (eds) Frontiers in Algorithmics. FAW 2017. Lecture Notes in Computer Science(), vol 10336. Springer, Cham. https://doi.org/10.1007/978-3-319-59605-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59605-1_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59604-4

  • Online ISBN: 978-3-319-59605-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation