Skip to main content

Very Fast Instances for Concept Generation

  • Conference paper
Formal Concept Analysis

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3874))

Abstract

Computing the maximal bicliques of a bipartite graph is equivalent to generating the concepts of the binary relation defined by the matrix of this graph. We study this problem for special classes of input relations for which concepts can be generated much more efficiently than in the general case; in some special cases, we can even say that the number of concepts is polynomially bounded, and all concepts can be generated particularly quickly.

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. Alexe, G., Alexe, S., Crama, Y., Foldes, S., Hammer, P.L., Simeone, B.: Consensus algorithm for the generation of all maximal bicliques. Discrete Applied Mathematics 145, 11–21 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Barbut, M., Monjardet, B.: Ordre et classification. Classiques Hachette (1970)

    Google Scholar 

  3. Berry, A., Bordat, J.-P., Sigayret, A.: Concepts can’t afford to stammer. In: INRIA Proc. International Conference ”Journées de l’Informatique Messine” (JIM 2003), Metz (France) (September 2003), Submitted as A local approach to concept generation

    Google Scholar 

  4. Berry, A., Sigayret, A.: Representing a concept lattice by a graph. Discrete Applied Mathematics 144(1-2), 27–42 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bordat, J.-P.: Calcul pratique du treillis de Galois d’une correspondance. Mathématiques, Informatique et Sciences Humaines 96, 31–47 (1986)

    MATH  MathSciNet  Google Scholar 

  6. Booth, S., Lueker, S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13, 335–379 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  7. Coppersmith, D., Winograd, S.: On the Asymptotic Complexity of Matrix Multiplication. SIAM J. Comput. 11(3), 472–492 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fulkerson, D.R., Gross, O.A.: Incidence matrices and interval graphs. Pacific J. Math. 15, 835–855 (1965)

    MATH  MathSciNet  Google Scholar 

  9. Ganter, B.: Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt (1984)

    Google Scholar 

  10. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  11. Kloks, T., Kratsch, D.: Computing a perfect edge without vertex elimination ordering of a chordal bipartite graph. Information Processing Letter 55, 11–16 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. Journal for Experimental and Theoretical Artificial Intelligence (JETAI) 14(2-3), 189–216 (2002)

    Article  MATH  Google Scholar 

  13. McConnell, R.M.: A certifying algorithm for the consecutive ones property. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), vol. 15, pp. 761–770 (2004)

    Google Scholar 

  14. Paige, R., Tarjan, R.E.: Three Partition Refinement Algorithms. SIAM Journal on Computing 16, 973–989 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Spinrad, J.P.: Efficient Graph Representation. Fields Institue Monographs, vol. 19. American Mathematical Society, Providence (2003)

    Google Scholar 

  16. Spinrad, J.P.: Doubly Lexical Orderings of Dense 0-1 Matrices. Information Processing Letters 45, 229–235 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zaki, M.J., Parthasarathy, S., Ogihara, M., Li, W.: New Algorithms for Fast Discovery of Association Rules. In: Proceedings of 3rd Int. Conf. on Database Systems for Advanced Applications (April 1997)

    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

Berry, A., McConnell, R.M., Sigayret, A., Spinrad, J.P. (2006). Very Fast Instances for Concept Generation. In: Missaoui, R., Schmidt, J. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671404_8

Download citation

  • DOI: https://doi.org/10.1007/11671404_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32203-0

  • Online ISBN: 978-3-540-32204-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics