Nothing Special   »   [go: up one dir, main page]

Skip to main content

Constructions and In-Place Operations for MDDs Based Constraints

  • Conference paper
  • First Online:
Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2016)

Abstract

This papers extends in three ways our previous work about efficient operations on Multi-valued Decision Diagrams (MDD) for building Constraint Programming models. First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds or sequences of tuples into MDDs. Then, we present in-place algorithms for adding and deleting tuples from an MDD. Finally, we describe an incremental version of an algorithm which reduces an MDD. We show on a real-life application that in-place operations on MDDs combined with this incremental algorithm outperform classical operations. Furthermore, we give some experimental results showing that the creation algorithms we propose strongly improve upon existing ones.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /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
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

Similar content being viewed by others

References

  1. Andersen, H.R., Hadzic, T., Hooker, J.N., Tiedemann, P.: A constraint store based on multivalued decision diagrams. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 118–132. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Bergman, D., Cire, A., van Hoeve, W.-J.: MDD propagation for sequence constraints. J. Artif. Intell. Res. 50, 697–722 (2014)

    MathSciNet  MATH  Google Scholar 

  3. Bergman, D., van Hoeve, W.-J., Hooker, J.N.: Manipulating MDD relaxations for combinatorial optimization. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 20–35. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Brace, K.S., Rudell, R.L., Bryant, R.E.: Efficient implementation of a BDD package. In: Proceedings of the 27th ACM/IEEE Design Automation Conference, pp. 40–45. ACM (1991)

    Google Scholar 

  5. Bryant, R.E.: Symbolic boolean manipulation with ordered binary decision diagrams. ACM Comput. Surv. 24(3), 293–318 (1992)

    Article  Google Scholar 

  6. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. C C35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  7. Cheng, K., Yap, R.: An MDD-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints. Constraints 15, 265–304 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cheng, K.C.K., Yap, R.H.C.: Maintaining generalized arc consistency on ad hoc r-ary constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 509–523. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Ciré, A.A., Hooker, J.N.: The separation problem for binary decision diagrams. In: International Symposium on Artificial Intelligence and Mathematics, ISAIM 2014, Fort Lauderdale, FL, USA, 6–8 January 2014

    Google Scholar 

  10. Focacci, F., Milano, M.: Global cut framework for removing symmetries. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 77–92. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Gange, G., Stuckey, P., Szymanek, R.: MDD propagators with explanation. Constraints 16, 407–429 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gent, I., Jefferson, C., Miguel, I., Nightingale, P.: Data structures for generalised arc consistency for extensional constraints. In: Proceedings of AAAI 2007, pp. 191–197, Vancouver, Canada (2007)

    Google Scholar 

  13. Hadzic, T., Hooker, J.N., O’Sullivan, B., Tiedemann, P.: Approximate compilation of constraints into multivalued decision diagrams. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 448–462. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Hoda, S., van Hoeve, W.-J., Hooker, J.N.: A systematic approach to MDD-based constraint programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 266–280. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Lhomme, O.: Practical reformulations with table constraints. In: ECAI, pp. 911–912 (2012)

    Google Scholar 

  16. Papadopoulos, A., Roy, P., Pachet, F.: Avoiding plagiarism in markov sequence generation. In: Proceeding of the Twenty-Eight AAAI Conference on Artificial Intelligence, pp. 2731–2737 (2014)

    Google Scholar 

  17. Perez, G., Régin, J.-C.: Improving GAC-4 for table and MDD constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 606–621. Springer, Heidelberg (2014)

    Google Scholar 

  18. Perez, G., Régin, J.-C.: Efficient operations on MDDs for building constraint programming models. In: International Joint Conference on Artificial Intelligence, IJCAI 2015, pp. 374–380, Argentina (2015)

    Google Scholar 

  19. Régin, J.-C.: Improving the expressiveness of table constraints. In: CP 2011, Proceedings Workshop ModRef 2011 (2011)

    Google Scholar 

  20. Srinivasan, A., Ham, T., Malik, S., Brayton, R.K.: Algorithms for discrete function manipulation. In: IEEE International Conference on Computer-Aided Design, ICCAD 1990. Digest of Technical Papers, pp. 92–95. IEEE (1990)

    Google Scholar 

Download references

Acknowledgments

We would like to thank very much Laurent Perron and Christophe Lecoutre for their useful comments which helped to improve the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean-Charles Régin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Perez, G., Régin, JC. (2016). Constructions and In-Place Operations for MDDs Based Constraints. In: Quimper, CG. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2016. Lecture Notes in Computer Science(), vol 9676. Springer, Cham. https://doi.org/10.1007/978-3-319-33954-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33954-2_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33953-5

  • Online ISBN: 978-3-319-33954-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics