Skip to main content

Approximation of coNP sets by NP-complete sets

  • Session 1A: Complexity Theory
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

Included in the following conference series:

Abstract

It is said that a set L 1 in a class C 1 approximates a set L 2 in a class C 2 if L 1 is a subset of L 2. Approximation L 1 is said to be optimal if there is no approximation L1 such that L1L 1 and L1 - L 1 is infinite. When C 1=P and C 2=NP, it is known that there is no optimal approximation under a quite general condition unless P=NP. In this paper we discuss the case where C 1=the class of NP-complete sets and C 2=coNP. A similar result as above that shows the difficulty of the optimal approximation is obtained. Approximating coNP sets by NP-complete sets play an important role in the efficient generation of test instances for combinatorial algorithms.

This research was supported by Scientific Research Grant, Ministry of Education, Japan, No. 04650318, and Engineering Adventure Group Linkage Program (EAGL), Japan.

Research Fellow of the Japan Society for the Promotion of Science. This research was supported by Scientific Research Grant, Ministry of Education, Japan, No. 2273

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. Y. Asahiro, K. Iwama and E. Miyano, “Random generation of test instances with controlled attributes,” In Proc. Second DIMACS Challenge Workshop, (M. Trick and D. Johnson, Ed.) American Mathematical Society, 1995.

    Google Scholar 

  2. J. Balcazar and J. Diaz and J. Gabarro, “Structural Complexity II,” Springer, 1989.

    Google Scholar 

  3. D. Bauer, S.L. Hakimi and E. Schmeichel, “Recognizing tough graphs is NP-hard,” Discrete Applied Mathematics, 28, pp. 191–195, 1990.

    Article  Google Scholar 

  4. V. Chvátal, “Hamiltonian cycles”, In The traveling salesman problem (John Wiley and Sons Ltd.), pp. 403–429, 1985.

    Google Scholar 

  5. S. Even and A. Selman and Y. Yacobi, “The complexity of promise problems with application to public-key cryptography,” Information and Control, 61, 1984.

    Google Scholar 

  6. J. Grollmann and A.L. Selman, “Complexity measures for public-key cryptosystems,” SIAM J. Comput., 17, pp. 309–334, 1988.

    Article  Google Scholar 

  7. K. Iwama and E. Miyano, “Security of test-case generation with known answers,” In Proc. AAAI Spring Symposium Series, 1993.

    Google Scholar 

  8. K. Iwama and E. Miyano, “Better approximations of non-Hamiltonian graphs,” manuscript, 1995.

    Google Scholar 

  9. K. Iwama and E. Miyano, “Intractability of read-once resolution,” In Proc. 10th IEEE Conference on Structure in Complexity Theory, 1995, to appear.

    Google Scholar 

  10. P. Orponen, D. Russo and U. Schoning, “Optimal approximations and polynomially levelable sets,” SIAM J. Comput., 15, pp.399–408, 1986.

    Article  Google Scholar 

  11. L. Sanchis, “Generating hard and diverse test sets for NP-hard graph problems,” Discrete Applied Mathematics, to appear.

    Google Scholar 

  12. T. Pitassi and A. Urquhart, “The complexity of Hajós calculus,” In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pp.187–196, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ding-Zhu Du Ming Li

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iwama, K., Miyazaki, S. (1995). Approximation of coNP sets by NP-complete sets. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030815

Download citation

  • DOI: https://doi.org/10.1007/BFb0030815

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics