The Regularization of Small Sub-Constraint Satisfaction Problems | SpringerLink
Skip to main content
Springer Nature Link
Log in

The Regularization of Small Sub-Constraint Satisfaction Problems

  • Conference paper
  • First Online:
Declarative Programming and Knowledge Management (INAP 2019, WLP 2019, WFLP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12057))

  • 325 Accesses

Abstract

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of fails in the resolution process, to improve the inferences made during search by the constraint solver by strengthening constraint propagation, and to maintain the level of propagation while reducing the cost of propagating the constraints. Our experimental results show improvements in terms of the resolution speed compared to the original CSPs and a competitiveness to the recent tabulation approach [1, 15]. Besides, our approach can be realized in a preprocessing step, and therefore wouldn’t collide with redundancy constraints or parallel computing if implemented.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • 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

Similar content being viewed by others

Notes

  1. 1.

    In [1], the detected constraints are substituted by table constraints, in contrast to the here presented approach; we will substitute them with regular constraints.

  2. 2.

    For case 8 exists a deterioration of 65% (90%, 95%) for the RegularIntersected (Table and Regular) approach. To keep the graphic small the negative values were drawn in \(\frac{1}{10}\) of the real distance. In cases 5, 25 and 46 none of the four models found a solution in the time bounds of 10 min.

References

  1. Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P., Salamon, A.Z.: Automatic discovery and exploitation of promising subproblems for tabulation. In: Hooker, J. (ed.) CP 2018. LNCS, vol. 11008, pp. 3–12. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98334-9_1

    Chapter  Google Scholar 

  2. Löffler, S., Liu, K., Hofstedt, P.: The power of regular constraints in CSPs. In: 47. Jahrestagung der Gesellschaft für Informatik, Informatik 2017, Chemnitz, Germany, 25–29 September 2017, pp. 603–614 (2017). https://doi.org/10.18420/in2017_57

  3. Löffler, S., Liu, K., Hofstedt, P.: The regularization of CSPs for rostering, planning and resource management problems. In: Iliadis, L., Maglogiannis, I., Plagianakos, V. (eds.) AIAI 2018. IAICT, vol. 519, pp. 209–218. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92007-8_18

    Chapter  Google Scholar 

  4. Löffler, S., Liu, K., Hofstedt, P.: A meta constraint satisfaction optimization problem for the optimization of regular constraint satisfaction problems. In: Rocha, A.P., Steels, L., van den Herik, J. (eds.) Proceedings of the 11th International Conference on Agents and Artificial Intelligence, ICAART 2019, Prague, Czech Republic, 19–21 February 2019, vol. 2, pp. 435–442. SciTePress (2019). https://doi.org/10.5220/0007260204350442

  5. Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI 2004, including Prestigious Applicants of Intelligent Systems, PAIS 2004, Valencia, Spain, 22–27 August 2004, pp. 146–150. IOS Press (2004)

    Google Scholar 

  6. Cheng, B.M.W., Lee, J.H.M., Wu, J.C.K.: Speeding up constraint propagation by redundant modeling. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 91–103. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61551-2_68

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  8. Dekker, J.J., Björdal, G., Carlsson, M., Flener, P., Monette, J.: Auto-tabling for subproblem presolving in MiniZinc. Constraints 22(4), 512–529 (2017). https://doi.org/10.1007/s10601-017-9270-5

    Article  MathSciNet  MATH  Google Scholar 

  9. Gent, I.: CSPLib problem 014: Solitaire battleships. http://www.csplib.org/Problems/prob014. Accessed 07 May 2019

  10. Gent, I.P., et al.: Search in the patience game ‘black hole’. AI Commun. 20(3), 211–226 (2007). http://content.iospress.com/articles/ai-communications/aic405

    MathSciNet  MATH  Google Scholar 

  11. Gottlob, G., Samer, M.: A backtracking-based algorithm for hypertree decomposition. J. Exp. Algorithmics (JEA) 13, 1 (2008)

    Google Scholar 

  12. Hamadi, Y.: Optimal distributed arc-consistency. Constraints 7(3–4), 367–385 (2002). https://doi.org/10.1023/A:1020594125144

    Article  MathSciNet  MATH  Google Scholar 

  13. Hellsten, L., Pesant, G., van Beek, P.: A domain consistency algorithm for the stretch constraint. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 290–304. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_23

    Chapter  MATH  Google Scholar 

  14. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Boston (1979)

    MATH  Google Scholar 

  15. Lecoutre, C.: STR2: optimized simple tabular reduction for table constraints. Constraints 16(4), 341–371 (2011). https://doi.org/10.1007/s10601-011-9107-6

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu, K., Löffler, S., Hofstedt, P.: Hypertree decomposition: the first step towards parallel constraint solving. In: Seipel, D., Hanus, M., Abreu, S. (eds.) WFLP/WLP/INAP -2017. LNCS (LNAI), vol. 10997, pp. 81–94. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00801-7_6

    Chapter  Google Scholar 

  17. Nightingale, P.: CSPLib problem 081: Black hole. http://www.csplib.org/Problems/prob081. Accessed 07 May 2019

  18. Pesant, G.: A filtering algorithm for the stretch constraint. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 183–195. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45578-7_13

    Chapter  MATH  Google Scholar 

  19. Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_36

    Chapter  MATH  Google Scholar 

  20. Prud’homme, C., Fages, J.G., Lorca, X.: Choco Documentation. TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S. (2016). http://www.choco-solver.org/. Accessed 07 May 2019

  21. Régin, J.-C., Rezgui, M., Malapert, A.: Embarrassingly parallel search. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 596–610. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40627-0_45

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, MINT, Programming Languages and Compiler Construction Group, Brandenburg University of Technology Cottbus-Senftenberg, Konrad-Wachsmann-Allee 5, 03044, Cottbus, Germany

    Sven Löffler, Ke Liu & Petra Hofstedt

Authors
  1. Sven Löffler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petra Hofstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sven Löffler .

Editor information

Editors and Affiliations

  1. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Petra Hofstedt

  2. Universidade de Évora, Évora, Portugal

    Salvador Abreu

  3. hwtk Berlin, Berlin, Germany

    Ulrich John

  4. Westfälische Wilhelms-Universität Münster, Münster, Germany

    Herbert Kuchen

  5. Universität Würzburg, Würzburg, Germany

    Dietmar Seipel

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Löffler, S., Liu, K., Hofstedt, P. (2020). The Regularization of Small Sub-Constraint Satisfaction Problems. In: Hofstedt, P., Abreu, S., John, U., Kuchen, H., Seipel, D. (eds) Declarative Programming and Knowledge Management. INAP WLP WFLP 2019 2019 2019. Lecture Notes in Computer Science(), vol 12057. Springer, Cham. https://doi.org/10.1007/978-3-030-46714-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-46714-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-46713-5

  • Online ISBN: 978-3-030-46714-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation