Skip to main content

Dynamic Bundling: Less Effort for More Solutions

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2371))

Abstract

Bundling of the values of variables in a Constraint Satisfaction Problem (CSP) as the search proceeds is an abstraction mechanism that yields a compact representation of the solution space. We have previously established that, in spite of the effort of recomputing the bundles, dynamic bundling is never less effective than static bundling and non-bundling search strategies. Objections were raised that bundling mechanisms (whether static or dynamic) are too costly and not worthwhile when one is not seeking all solutions to the CSP. In this paper, we dispel these doubts and empirically show that (1) dynamic bundling remains superior in this context, (2) it does not require a full lookahead strategy, and (3) it dramatically reduces the cost of solving problems at the phase transition while yielding a bundle of multiple, robust solutions.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amy M. Beckwith and Berthe Y. Choueiry. On the Dynamic Detection of Inter-changeability in Finite Constraint Satisfaction Problems. In T. Walsh, editor, 7 th International Conference on Principle and Practice of Constraint Programming (CP’01), LNCS Vol. 2239, page 760, Paphos, Cyprus, 2001. Springer Verlag.

    Google Scholar 

  2. Amy M. Beckwith, Berthe Y. Choueiry, and Hui Zou. How the Level of Inter-changeability Embedded in a Finite Constraint Satisfaction Problem Affects the Performance of Search. In 14th Australian Joint Conference on Artificial Intelligence. LNAI Vol. 2256, pages 50–61, Adelaide, Australia, 2001. Springer Verlag.

    Google Scholar 

  3. Cynthia A. Brown, Larry Finkelstein, and Paul W. Purdom, Jr. Backtrack Searching in the Presence of Symmetry. In T. Mora, editor, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pages 99–110. Springer-Verlag, 1988.

    Google Scholar 

  4. Peter Cheeseman, Bob Kanefsky, and William M. Taylor. Where the Really Hard Problems Are. In Proc. of the 12 th IJCAI, pages 331–337, Sidney, Australia, 1991.

    Google Scholar 

  5. Berthe Y. Choueiry and Amy M. Beckwith. On Finding the First Solution Bundle in Finite Constraint Satisfaction Problems. Technical Report CSL-01-03. consystlab.unl.edu/CSL-01-04.ps, University of Nebraska-Lincoln, 2001.

    Google Scholar 

  6. Berthe Y. Choueiry, Boi Faltings, and Rainer Weigel. Abstraction by Interchangeability in Resource Allocation. In Proc. of the 14 th IJCAI, pages 1694–1701, Montréal, Québec, Canada, 1995.

    Google Scholar 

  7. Berthe Y. Choueiry and Guevara Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. Technical Report KSL-98-24, Knowledge Systems Laboratory, Department of Computer Science, Stanford University, Stanford, CA, 1998. Preliminary version in Proc. of AAAI’98

    Google Scholar 

  8. Thomas Ellman. Abstraction via Approximate Symmetry. In Proc. of the 13 th IJCAI, pages 916–921, Chambéry, France, 1993.

    Google Scholar 

  9. Jay P. Fillmore and S.G. Williamson. On Backtracking: A Combinatorial Description of the Algorithm. SIAM Journal on Computing, 3(1):41–55, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  10. Eugene C. Freuder. Eliminating Interchangeable Values in Constraint Satisfaction Problems. In Proc. of AAAI-91, pages 227–233, Anaheim, CA, 1991.

    Google Scholar 

  11. Ian P. Gent and Patrick Prosser. Inside MAC and FC. Technical Report APES-20-2000, APES Research Group, 2000.

    Google Scholar 

  12. Matthew L. Ginsberg, Andrew J. Parkes, and Amitabha Roy. Supermodels and Robustness. In Proc. of AAAI-98, pages 334–339, Madison, Wisconsin, 1998.

    Google Scholar 

  13. J.W.L. Glaisher. On the Problem of the Eight Queens. Philosophical Magazine, series 4, 48:457–467, 1874.

    Google Scholar 

  14. Alois Haselböck. Exploiting Interchangeabilities in Constraint Satisfaction Problems. In Proc. of the 13 th IJCAI, pages 282–287, Chambéry, France, 1993.

    Google Scholar 

  15. Tad Hogg, Bernardo A. Hubermann, and Colin P. Williams editors. Special Volume on Frontiers in Problem Solving: Phase Transitions and Complexity, volume 81(1–2). Elsevier Science, 1996.

    Google Scholar 

    Google Scholar 

  16. Jean-Francois Puget. On the Satisfiability of Symmetrical Constrained Satisfaction Problems. In ISMIS’93, pages 350–361, 1993.

    Google Scholar 

  17. Daniel Sabin and Eugene C. Freuder. Contradicting Conventional Wisdom in Constraint Satisfaction. In Proc. of the 11 th ECAI, pages 125–129, Amsterdam, The Netherlands, 1994.

    Google Scholar 

  18. M-C. Silaghi, D. Sam-Haroud, and B. Faltings. Ways of Maintaining Arc Consistency in Search using the Cartesian Representation. In Proc. of ERCIM’99, LNAI, Paphos, Cyprus, 1999. Springer Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Choueiry, B.Y., Davis, A.M. (2002). Dynamic Bundling: Less Effort for More Solutions. In: Koenig, S., Holte, R.C. (eds) Abstraction, Reformulation, and Approximation. SARA 2002. Lecture Notes in Computer Science(), vol 2371. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45622-8_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45622-8_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43941-7

  • Online ISBN: 978-3-540-45622-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics