Skip to main content

On Dualization in Products of Forests

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

Abstract

Let P = P 1 ×…×P n be the product of n partially ordered sets, each with an acyclic precedence graph in which either the in-degree or the out-degree of each element is bounded. Given a subset AP, it is shown that the set of maximal independent elements of A in P can be incrementally generated in quasi-polynomial time. We discuss some applications in data mining related to this dualization problem.

Partially supported by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science.

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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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. R. Agrawal, T. Imielinski and A. Swami, Mining association rules between sets of items in massive databases. In Proc. the 1993 ACM-SIGMOD Int. Conf. Management of Data, pp. 207–216.

    Google Scholar 

  2. R. Agrawal and R. Srikant, Fast algorithms for mining association rules in large databases. In Proc. 20th Int. Conf. Very Large Data Bases, pp. 487–499, 1994.

    Google Scholar 

  3. R. Agrawal and R. Srikant, Mining sequential patterns. In Proc. 11th Int. Conf. Data Engineering, pp. 3–14, 1995.

    Google Scholar 

  4. R. Agrawal, H. Mannila, R. Srikant, H. Toivonen and A. I. Verkamo, Fast discovery of association rules. In Advancesin Knowledge Discovery and Data Mining, pp. 307–328, AAAI Press, Menlo Park, California, 1996.

    Google Scholar 

  5. M. Anthony and N. Biggs, Computational Learning Theory, Cambridge University Press, 1992.

    Google Scholar 

  6. J. C. Bioch and T. Ibaraki, Complexity of identification and dualization of positive Boolean functions, Information and Computation, 123 (1995) pp. 50–63.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Boros, K. Elbassioni, V. Gurvich, L. Khachiyan and K. Makino, On generating all minimal integer solutions for a monotone system of linear inequalities. In Automata, Languagesand Programming, 28th Int. Colloquium, ICALP 2001,LNCS 2076, pp. 92–103 (Springer Verlag, Berlin, Heidelberg, New York, July 2001).

    Chapter  Google Scholar 

  8. E. Boros, V. Gurvich, L. Khachiyan and K. Makino, An inequality limiting the number of maximal frequent sets, DIMACS tech. report 2000-37, Rutgers Univ.

    Google Scholar 

  9. E. Boros, V. Gurvich, L. Khachiyan and K. Makino, Generating weighted transversals of a hypergraph, in Proceedings of the 2nd Japanese-Hungarian Symposium on Discrete Mathematicsand ItsApplic ations, pp. 13–22, Hungarian Academy of Sciences, Budapest, Hungary, April 20–23, 2001.

    Google Scholar 

  10. S. Brin, R. Motwani and C. Silverstein, Beyond market basket: Generalizing association rules to correlations. In Proc. the 1997 ACM-SIGMOD Int. Conf. Management of Data, pp. 265–276.

    Google Scholar 

  11. C. J. Colbourn, The combinatoricsof network reliability, Oxford Univ. Press, 1987.

    Google Scholar 

  12. T. Eiter and G. Gottlob, Identifying the minimal transversals of a hypergraph and related problems, SIAM Journal on Computing, 24 (1995) pp. 1278–1304.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. L. Fredman and L. Khachiyan, On the complexity of dualization of monotone disjunctive normal forms, Journal of Algorithms, 21 (1996) pp. 618–628.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Gunopulos, R. Khardon, H. Mannila, and H. Toivonen, Data mining, hypergraph transversals and machine learning. In Proc. 16th ACM-SIGACT-SIGMODSIGART Symposium on Principles of Database Systems, (1997) pp. 12–15.

    Google Scholar 

  15. V. Gurvich and L. Khachiyan, On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions, Discrete Applied Mathematics, 1996–97, issue 1–3, (1999) pp. 363–373.

    Google Scholar 

  16. J. Han and Y. Fu, Discovery of multiple-level association rules from large databases. In Proc. 21st Int. Conf. Very Large Data Bases, pp. 420–431, 1995.

    Google Scholar 

  17. K. Makino and T. Ibaraki, Interior and exterior functions of Boolean functions, Discrete Applied Mathematics, 69 (1996) pp. 209–231.

    Article  MATH  MathSciNet  Google Scholar 

  18. H. Mannila, and H. Toivonen, Discovery of frequent episodes in event sequences, Data Mining and Knowledge Discovery, 1 (1997) pp. 259–289.

    Article  Google Scholar 

  19. R. C. Read, Every one a winner, or how to avoid isomorphism when cataloging combinatorial configurations, Annalsof Discrete Math. 2 (1978) pp. 107–120.

    Article  MATH  MathSciNet  Google Scholar 

  20. R. Srikant and R. Agrawal, Mining generalized association rules. In Proc. 21st Int. Conf. Very Large Data Bases, pp. 407–419, 1995.

    Google Scholar 

  21. R. Srikant and R. Agrawal, Mining quantitative association rules in large relational tables. In Proc. of the ACM-SIGMOD 1996 Int. Conf. Management of Data, pp. 1–12, 1996.

    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

Elbassioni, K.M. (2002). On Dualization in Products of Forests. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-45841-7_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics