Skip to main content

On Generators of Random Quasigroup Problems

  • Conference paper
Book cover Recent Advances in Constraints (CSCLP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3978))

Abstract

Problems that can be sampled randomly are a good source of test suites for comparing quality of constraint satisfaction techniques. Quasigroup problems are representatives of structured random problems that are closer to real-life problems and hence more suitable for benchmarking. In this paper, we describe in detail generators for Quasigroup Completion Problem (QCP) and Quasigroups with Holes (QWH). In particular, we study an improvement of the generator for QCP that produces a larger number of satisfiable problems by using propagation through the all-different constraint. We also re-formulate the algorithm for generating QWH that is much faster than the original generator. Finally, we provide an experimental comparison of all presented generators.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Achlioptas, D., Gomes, C., Kautz, H., Selman, B.: Generating Satisfiable Problem Instances. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 256–261. AAAI Press, Menlo Park (2000)

    Google Scholar 

  2. Barták, R., Rudová, H.: Limited Assignments: A New Cutoff Strategy for Incomplete Depth-First Search. In: Proceedings of the 2005 ACM Symposium on Applied Computing, pp. 388–392. ACM Press, New York (2005)

    Chapter  Google Scholar 

  3. Carlsson, M., Ottosson, G., Carlson, B.: An Open-ended Finite Domain Constraint Solver. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, Springer, Heidelberg (1997)

    Google Scholar 

  4. Colbourn, C.: The Complexity of Completing Partial Latin Squares. Discrete Applied Mathematics 8, 25–30 (1984)

    Article  MATH  Google Scholar 

  5. Dotú, I., del Val, A., Cebrián, M.: Channeling Constraints and Value Ordering in the Quasigroup Completion Problem. In: Proceedings of Eighteenth International Joint Conference on Artificial Inteligence, pp. 1372–1373. Morgan Kaufmann Publishers, San Francisco (2003)

    Google Scholar 

  6. Gomez, C., Selman, B.: Problem Structure in the Presence of Perturbations. In: Proceedings of Fourteenth National Conference on Artificial Intelligence, pp. 221–226. AAAI Press, Menlo Park (1997)

    Google Scholar 

  7. Gomez, C., Shmoys, D.: Completing Quasigroups or Latin Squares: A Structured Graph Coloring Problem. In: Proceedings Computational Symposium on Graph Coloring and Generalizations (2002)

    Google Scholar 

  8. Gomez, C., Shmoys, D.: The Promise of LP to Boost CSP Techniques for Combinatorial Problems. In: Proceedings CPAIOR 2002, pp. 291–305 (2002)

    Google Scholar 

  9. Jacobson, M.T., Matthews, P.: Generating Uniformly Distributed Random Latin Squares. Journal of Combinatorial Designs 4, 405–437 (1996)

    Article  MATH  Google Scholar 

  10. Kumar, S.K., Russell, A., Sundaram, R.: Approximating Latin Square Extensions. Algorithmica 24, 128–138 (1999)

    Article  MATH  Google Scholar 

  11. MacIntyre, E., Prosser, P., Smith, B., Walsh, T.: Random Constraint Satisfaction: theory meets practice. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 325–339. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  12. Meseguer, P., Walsh, T.: Interleaved and Discrepancy Based Search. In: Proceedings of 13th European Conference on Artificial Intelligence, pp. 239–243. Wiley, Chichester (1998)

    Google Scholar 

  13. Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of Twelfth National Conference on Artificial Intelligence, pp. 362–367. AAAI Press, Menlo Park (1994)

    Google Scholar 

  14. Shaw, P., Stergiou, K., Walsh, T.: Arc Consistency and Quasigroup Completion. In: Proceedings of the ECAI-1998 workshop on non-binary constraints (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barták, R. (2006). On Generators of Random Quasigroup Problems. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2005. Lecture Notes in Computer Science(), vol 3978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11754602_12

Download citation

  • DOI: https://doi.org/10.1007/11754602_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34215-1

  • Online ISBN: 978-3-540-34216-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics