Skip to main content
Log in

Asymptotically optimal dualization algorithms

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The design of efficient on average algorithms for discrete enumeration problems is studied. The dualization problem, which is a central enumeration problem, is considered. New asymptotically optimal dualization algorithms are constructed. It is shown that they are superior in time costs to earlier constructed asymptotically optimal dualization algorithms and other available dualization algorithms with different design features.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. Johnson, M. Yannakakis, and C. Papadimitriou, “On generating all maximal independent sets,” Inf. Proc. Lett. 27(3), 119–123 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Eiter, G. Gottlob, and K. Makino, “New results on monotone dualization and generating hypergraph transversals,” SIAM J. Comput. 32(2), 514–537 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  3. M. L. Fredman and L. Khachiyan, “On the complexity of dualization of monotone disjunctive normal forms,” J. Algorithms 21, 618–628 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Khachiyan, E. Bows, K. Elbassioni, and V. Gurvich, “An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals and its application in joint generation,” Discrete Appl. Math. 154(16), 2350–2372 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Boros and K. Elbassioni, “Generating maximal independent sets for hypergraphs with bounded edge-intersections,” LATIN 2004: Theoretical Informatics (Springer, Berlin, 2004), pp. 488–498.

    Chapter  Google Scholar 

  6. E. Boros, V. Gurvich, K. Elbassioni, and L. Khachiyan, “An efficient incremental algorithm for generating all maximal independent sets in hypergraphs of bounded dimension,” Parallel Process. Lett. 10(4), 253–266 (2000).

    Article  MathSciNet  Google Scholar 

  7. E. V. Djukova, “Asymptotically optimal algorithm for constricting irredundant tests,” Dokl. Akad. Nauk SSSR 233(4), 527–530 (1977).

    MathSciNet  Google Scholar 

  8. E. V. Djukova, “Discrete recognition procedures: The complexity of realization,” Pattern Recogn. Image Anal. 13(1), 8–10 (2003).

    Google Scholar 

  9. E. V. Djukova and R. M. Sotnezov, “On the complexity of discrete generation problems,” Dokl. Math. 82(3), 847–849 (2010).

    Article  MathSciNet  Google Scholar 

  10. E. V. Djukova and Yu. I. Zhuravlev, “Discrete methods of information analysis in recognition and algorithm synthesis,” Pattern Recogn. Image Anal. 7(2), 192–207 (1997).

    Google Scholar 

  11. E. V. Djukova, “The Complexity of the Realization of Certain Recognition Procedures,” USSR Comput. Math. Math. Phys. 27(1), 74–83 (1987).

    Article  Google Scholar 

  12. E. V. Djukova, “On the implementation complexity of discrete (logical) recognition procedures,” Comput. Math. Math. Phys. 44(3), 532–541 (2004).

    MathSciNet  Google Scholar 

  13. E. V. Djukova and Yu. I. Zhuravlev, “Discrete analysis of feature descriptions in recognition problems of high dimensionality,” Comput. Math. Math. Phys. 40(8), 1214–1227 (2000).

    MathSciNet  Google Scholar 

  14. E. V. Djukova and A. S. Inyakin, “Asymptotically optimal construction of irredundant coverings of an integer matrix,” Mat. Voprosy Kibern. 17, 235–246 (2008).

    Google Scholar 

  15. E. V. Djukova and P. M. Sotnezov, “On the complexity of the dualization problem,” Comput. Math. Math. Phys. 52(10), 1472–1481 (2012).

    Article  MathSciNet  Google Scholar 

  16. E. V. Djukova and P. A. Prokofjev, “On asymptotically optimal enumeration for irreducible coverings of a Boolean matrix,” Prikl. Diskret. Mat., No. 1, 96–105 (2014).

    Google Scholar 

  17. K. Murakami and T. Uno, “Efficient Algorithms for Dualizing Large-Scale Hypergraphs,” Proc, 15.

  18. K. Murakami and T. Uno, “Efficient algorithms for dualizing large-scale hypergraphs,” Discrete Appl. Math. 170, 83–94 (2014).

    Article  MATH  MathSciNet  Google Scholar 

  19. UCI machine learning repository; http://archive.ics.uci.edu/ml/.

  20. Frequent itemset mining dataset repository; http://fimi.ua.ac.be/data/.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. V. Djukova.

Additional information

Original Russian Text © E.V. Djukova, P.A. Prokofjev, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 5, pp. 895–910.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Djukova, E.V., Prokofjev, P.A. Asymptotically optimal dualization algorithms. Comput. Math. and Math. Phys. 55, 891–905 (2015). https://doi.org/10.1134/S0965542515050103

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542515050103

Keywords

Navigation