Skip to main content
Book cover

Ibero-American Conference on Artificial Intelligence

IBERAMIA 2008: Advances in Artificial Intelligence – IBERAMIA 2008 pp 73–82Cite as

Using Indexed Finite Set Variables for Set Bounds Propagation

  • Conference paper

  • 1144 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 5290)

Abstract

Constraint Programming (CP) has been successfully applied to numerous combinatorial problems such as scheduling, graph coloring, circuit analysis, or DNA sequencing. Following the success of CP over traditional domains, set variables were also introduced to more declaratively solve a number of different problems.

Using a bounds representation for a finite set variable allows one to compactly represent the solution set of a set constraint problem. Many consistency mechanisms for maintaining bounds consistency have been proposed and in this paper we propose to use delta domain variable information to speed up constraint propagation. Additionally, we propose the use of indexed set domain variable representations as a better means of improving the use, intuitiveness and efficiency of delta domain variables for propagation tasks.

Keywords

  • finite set constraint variables
  • graph constraint variables
  • constraint propagation
  • delta domain variables
  • indexation

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-88309-8_8
  • Chapter length: 10 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-88309-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.00
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gervet, C.: Interval Propagation to Reason about Sets: Definition and Implementation of a Practical Language. Constraints journal 1(3), 191–244 (1997)

    MATH  CrossRef  MathSciNet  Google Scholar 

  2. Azevedo, F.: Cardinal: A finite sets constraint solver. Constraints journal 12(1), 93–129 (2007)

    MATH  CrossRef  Google Scholar 

  3. ECLiPSE Constraint System, http://eclipse.crosscoreop.com/

  4. Correia, M., Barahona, P., Azevedo, F.: Casper: A programming environment for development and integration of constraint solvers. In: Azevedo, F., Gervet, C., Pontelli, E. (eds.) Proceedings of the First International Workshop on Constraint Programming Beyond Finite Integer Domains (BeyondFD 2005), pp. 59–73 (2005)

    Google Scholar 

  5. CaSPER: Constraint Solving Programming Environment for Research, http://proteina.di.fct.unl.pt/casper/

  6. Azevedo, F.: Constraint Solving over Multi-Valued Logics. Frontiers in Artificial Intelligence and Applications, vol. 91. IOS Press, Amsterdam (2003)

    MATH  Google Scholar 

  7. Lagerkvist, M., Schulte, C.: Advisors for incremental propagation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 409–422. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  8. Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph CSPs. In: Lee, J., Stuckey, P. (eds.) Proceedings of the Sixth International Workshop on Constraint Modelling and Reformulation (ModRef 2007), Providence, Rhode Island, USA (September 2007)

    Google Scholar 

  9. Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph Constraint Satisfaction Problems. In: Analide, C., Novais, P., Henriques, P. (eds.) Simpósio Doutoral em Inteligência Artificial, Guimarães, Portugal (December 2007)

    Google Scholar 

  10. Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph Constraint Satisfaction Problems. In: Azevedo, F., Lynce, I., Manquinho, V. (eds.) Search Techniques for Constraint Satisfaction, Guimarães, Portugal (December 2007)

    Google Scholar 

  11. Viegas, R.D.: Constraint Solving over Finite Graphs. Master’s thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa (2008)

    Google Scholar 

  12. Padberg, M.W.: Covering, Packing and Knapsack Problems. Annals of Discrete Mathematics, vol. 4 (1979)

    Google Scholar 

  13. Beasley, J.: An algorithm for set covering problems. European Journal of Operational Research 31, 85–93 (1987)

    MATH  CrossRef  MathSciNet  Google Scholar 

  14. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  15. Beasley, J.: A Lagrangian Heuristic for Set-Covering problems. Naval Research Logistics (NRL) 37(1), 151–164 (1990)

    MATH  CrossRef  MathSciNet  Google Scholar 

  16. Mathews, C., van Holde, K.: Biochemistry, 2nd edn. Benjamin Cummings (1996)

    Google Scholar 

  17. Attwood, T., Parry-Smith, D.: Introduction to Bioinformatics. Prentice-Hall, Englewood Cliffs (1999)

    Google Scholar 

  18. Sellmann, M.: Cost-based filtering for shorter path constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 694–708. Springer, Heidelberg (2003)

    Google Scholar 

  19. Dooms, G.: The CP(Graph) Computation Domain in Constraint Programming. PhD thesis, Faculté des Sciences Appliquées, Université Catholique de Louvain (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CENTRIA, Departamento de Informática Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa,  

    Ruben Duarte Viegas, Marco Correia, Pedro Barahona & Francisco Azevedo

Authors
  1. Ruben Duarte Viegas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Correia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pedro Barahona
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Francisco Azevedo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ICREA & Universitat Pompeu Fabra, Paseo de Circumvalacion 8, 08003, Barcelona, Spain

    Hector Geffner

  2. IST-UTL and INESC-ID, Av. Prof. Cavaco Silva - Taguspark, 2744-016, Porto Salvo, Portugal

    Rui Prada

  3. ADETTI/ISCTE and ISCTE, Lisbon University Institute, Av. das Forças Armadas, 1649-026, Lisbon, Portugal

    Isabel Machado Alexandre

  4. ADETTI/ISCTE and ISCTE, Lisbon University Institute, , Av. das Forças Armadas, 1649-026, Lisbon, Portugal

    Nuno David

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Viegas, R.D., Correia, M., Barahona, P., Azevedo, F. (2008). Using Indexed Finite Set Variables for Set Bounds Propagation. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds) Advances in Artificial Intelligence – IBERAMIA 2008. IBERAMIA 2008. Lecture Notes in Computer Science(), vol 5290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88309-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88309-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88308-1

  • Online ISBN: 978-3-540-88309-8

  • eBook Packages: Computer ScienceComputer Science (R0)