Skip to main content

The complexity of learning minor closed graph classes

  • Conference paper
  • First Online:
Book cover Algorithmic Learning Theory (ALT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 997))

Included in the following conference series:

Abstract

The paper considers the problem of learning classes of graphs closed under taking minors. It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries. The representation of the class is in terms of a set of minimal excluded minors (obstruction set). Moreover, a negative result for learning such classes using only equivalence queries is also provided, after introducing a notion of reducibility among query learning problems.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Angluin. Queries and Concept Learning, Machine Learning, 2 (1988) 319–342.

    Google Scholar 

  2. D. Angluin. Negative results for equivalence queries. Machine Learning, 5 (1990) 121–150.

    Google Scholar 

  3. L. Hellerstein, and M. Karpinski. Learning read-once formulas with membership queries. Proc. of the 2nd COLT, San Mateo, CA, (1989), 162–174.

    Google Scholar 

  4. P. Auer, N. Cesa-Bianchi. On-Line Learning with Malicious Noise and the Closure Algorithm Proc. of the 5th International Workshop on Algorithmic Learning Theory, LNAI, 872 (1994) 229–247. To appear in Annals of AI and Mathematics

    Google Scholar 

  5. H.L. Bodlaender. A Tourist Guide through Treewidth, Acta Cybernetica, 11 (1993).

    Google Scholar 

  6. C. Domingo. Improved Fingerprints, Unpublished Manuscript, (1994).

    Google Scholar 

  7. R. Gavaldà. On the Power of Equivalence Queries. Proc. of the First European Conference in Computational Learning Theory, (1993), 193–203.

    Google Scholar 

  8. M.R. Fellows and M.A. Langston. Exploiting RS-posets: Constructive algorithms from nonconstructive tools. Preprint, Feb. 1989.

    Google Scholar 

  9. K. Makino and T. Ibaraki. A Fast and Simple Algorithm for Identifying 2-Monotonic Positive Boolean Functions Technical Report of IEICE, COMP94-46 (1994) 11–20.

    Google Scholar 

  10. L. Pitt and M. K. Warmuth, Prediction-Preserving Reducibility Journal of Computer Science, 41, (1990), 430–467.

    Google Scholar 

  11. N. Robertson and P.D. Seymour. Graph minors. I. Excluding a forest. J. Comb. Theory Series B, 35 (1983) 39–61.

    Google Scholar 

  12. N. Robertson and P.D. Seymour. Graph minors. III. Planar tree-width. J. Comb. Theory Series B, 36 (1984) 49–64.

    Article  Google Scholar 

  13. N. Robertson and P.D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms, 7 (1986) 309–322.

    Article  Google Scholar 

  14. N. Robertson and P.D. Seymour. Graph minors. V. Excluding a planar graph. J. Comb. Theory Series B, 41 (1986) 92–114.

    Google Scholar 

  15. N. Robertson and P.D. Seymour. Graph minors. IV. Tree-width and well-quasiordering. J. Comb. Theory Series B, 48 (1990) 227–254.

    Google Scholar 

  16. John Shawe-Taylor, Carlos Domingo, Hans Bodlaender and James Abello, Learning Minor Closed Graph Classes with Membership and Equivalence Queries, Neuro COLT Technical Report NC-TR-94-014, 1994.

    Google Scholar 

  17. O. Watanabe. A formal study of learning via queries. Lecture Notes in Computer Science 443: Proceedings of the 17th ICALP,M.S.Paterson, ed., Springer-Verlag, (1990) 139–152.

    Google Scholar 

  18. O. Watanabe. A framework for polynomial time query learnability Math. Systems Theory, 27 (1994) 211–229.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Klaus P. Jantke Takeshi Shinohara Thomas Zeugmann

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Domingo, C., Shawe-Taylor, J. (1995). The complexity of learning minor closed graph classes. In: Jantke, K.P., Shinohara, T., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1995. Lecture Notes in Computer Science, vol 997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60454-5_43

Download citation

  • DOI: https://doi.org/10.1007/3-540-60454-5_43

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60454-9

  • Online ISBN: 978-3-540-47470-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics