Skip to main content

A Novel Approach to the Minimal Cover Problem

  • Conference paper
Rough Sets, Fuzzy Sets and Knowledge Discovery

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

  • 205 Accesses

Abstract

Approximation algorithms for the Minimal Cover Problem (MCP) are presented in this paper. Contrary to the greedy approximation algorithm for MCP [Jo-74], [Lo-75], [Co-92], novel approaches to MCP are based on the simulated annealing (SA) and genetic algorithms (GA). The main difference between the existing technique and the new method is that the former algorithm gives one solution whereas the latter algorithms improves simultaneously several solutions. This property is important, particularly in the context of the problem of dependence relation of attributes in information systems [Pa-82], [Sk-92].

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. E.H.L. Aarts, J.H.M. Korst “Simulated Annealing and Boltzmann Machines” John Wiley & Sons 1989.

    Google Scholar 

  2. T.H. Cormen, C.E. Leiserson, R.L. Riverst “Introduction to Algorithms” MIT Press 1992.

    Google Scholar 

  3. Ed. by L. Davis “Genetic Algorithms and Simulated Annealing” Pitman, Morgan Kaufmann 1987.

    Google Scholar 

  4. D. Goldberg “Genetic Algorithms in Search, Optimization, and Machine Learning” Addison—Wesley 1982.

    Google Scholar 

  5. Jo-74] D.S. Johnson “Approximation Algorithms for Combinatorial Problems” Journal of Computer and System Science 9, 1974.

    Google Scholar 

  6. P.J.M. Laarhoven, E.H.L. Aarts “Simulated Annealing Theory and Application” Kluwer, Dordrecht Netherlands 1987.

    Google Scholar 

  7. L. Lovasz “On the radio of optimal integeral and fractional cover” Discrete Math. 13, 1975.

    Google Scholar 

  8. R. Motwani “Approximation Algorithms” (lecture notes) Stanford University 1991/1992.

    Google Scholar 

  9. Z. Pawlak “Rough Sets” International Journal of Computer and Information Science, vol. 11, No. 5, 1982.

    Google Scholar 

  10. P. Sapiecha “An Approximation Algorithm for Minimal Reduct Problem ” Proc. of the First Workshop on Rough Set Theory. Poland 1992; and also in Foundations of Computing and Decision Science vol. 18, No. 3 /4, 1993.

    Google Scholar 

  11. A. Skowron, C. Rauszer “The Discernibility Matrices and Functions in Information Systems” Handbook of Applications and Advances of the Rough Set Theory, ed. Slowinski R., Kluwer 1992.

    Google Scholar 

  12. M. Syslo, N. Deo, J. Kowalik “Discrete optimization algorithms with Pascal programs” Englewood Cliffs, NJ; Prentice Hall, 1983.

    Google Scholar 

  13. V. Zissimopoulos, V.Th. Paschos, F. Pekergin “On the approximation of NP—complete problems by using the Boltzmann Machine method: The cases of some covering and packing problems ” IEEE Trans on Comp. vol. 40, No. 12, December 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 British Computer Society

About this paper

Cite this paper

Sapiecha, P. (1994). A Novel Approach to the Minimal Cover Problem. In: Ziarko, W.P. (eds) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3238-7_28

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-3238-7_28

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19885-7

  • Online ISBN: 978-1-4471-3238-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics