Skip to main content

On the structure of parameterized problems in NP

Extended abstract

  • Conference paper
  • First Online:
STACS 94 (STACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

Included in the following conference series:

Abstract

Fixed-parameter intractability of optimization problems in NP is studied based on computational models with limited nondeterminism. Strong evidence is shown that many NP optimization problems are not fixed-parameter tractable and that the fixed-parameter intractability hierarchy (the W-hierarchy) does not collapse.

Cai is supported in part by Engineering Excellence Award from Texas A&M University; Chen is supported in part by NSF Grant CCR-9110824; Downey is supported in part by a grant from the Victoria University IGC, by the United States/New Zealand Cooperative Science Foundation under grant INT 90-20558, and by the Mathematical Sciences Institute at Cornell and Cornell University; and Fellows is supported in part by the National Science and Engineering Research Council of Canada, and by the United States NSF under grant MIP-8919312.

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.

Similar content being viewed by others

References

  1. K. Abrahamson, R. G. Downey and M. R. Fellows, Fixed-parameter intractability II, Lecture Notes in Computer Science (STACS'93), (1993), pp. 374–385.

    Google Scholar 

  2. K. R. Abrahamson, J. A. Ellis, M. R. Fellows, and M. E. Mata, On the complexity of fixed parameter problems, Proc. 30th Annual Symposium on Foundations of Computer Science, (1989), pp. 210–215.

    Google Scholar 

  3. S. Arnborg, J. Lagergren, and D. Seese, Problems easy for tree-decomposable graphs, Lecture Notes in Computer Science 317 (ICALP'88), (1988), pp. 38–51.

    Google Scholar 

  4. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and intractability of approximation problems, Proc. 33rd Annual Symposium on Foundations of Computer Science, (1992), pp. 14–23.

    Google Scholar 

  5. J. Balcazar, J. Diaz, and J. Gabarro, Structural Complexity I, Springer-Verlag, 1988.

    Google Scholar 

  6. R. B. Boppana and M. Sipser, The complexity of finite functions, in Handbook of Theoretical Computer Science, Vol. A, J. van Leeuwen, ed., (1990), pp. 757–804.

    Google Scholar 

  7. J. F. Buss and J. Goldsmith, Nondeterminism within P, SIAM J. Comput. 22, (1993), pp. 560–572.

    Google Scholar 

  8. S. Buss, Personal communication, (1992).

    Google Scholar 

  9. L. Cai and J. Chen, On input read-modes of alternating Turing machines, Technique Report 93–046, Dept. Computer Science, Texas A&M University, (1993).

    Google Scholar 

  10. L. Cai and J. Chen, Fixed parameter tractability and approximability of NP- hard optimization problems, Proc. 2rd Israel Symposium on Theory of Computing and Systems, (1993), pp. 118–126.

    Google Scholar 

  11. L. Cai and J. Chen, On the amount of nondeterminism and the power of verifying, Lecture Notes in Computer Science 711 (MFCS'93), (1993), pp. 311–320.

    Google Scholar 

  12. L. Cai, J. Chen, R. G. Downey, and M. R. Fellows, Advice classes of parameterized tractability, Proc. Asian Logic Conference, (1993).

    Google Scholar 

  13. J. Diaz and J. Toran, Classes of bounded nondeterminism, Mathematical Systems Theory 23, (1990), pp. 21–32.

    Google Scholar 

  14. R. G. Downey, P. A. Evans, and M. R. Fellows, Parameterized learning complexity, Proc. 6th ACM Workshop on Computational Learning Theory (COLT'93), (1993), pp. 51–57.

    Google Scholar 

  15. R. G. Downey and M. R. Fellows, Fixed-parameter intractability, Proc. 7th Structure in Complexity Theory Conference, (1992), pp. 36–49.

    Google Scholar 

  16. R. G. Downey and M. R. Fellows, Fixed parameter tractability and completeness, in Complexity Theory: Current Research, Ambos-Spies et al., ed., Cambridge University Press, (1993), pp. 191–225.

    Google Scholar 

  17. M. R. Fellows, M. T. Hallett, and H. T. Wareham, DNA physical mapping: three ways of difficult, Proc. 1st European Symposium on Algorithms, (1993), 157–168.

    Google Scholar 

  18. M. R. Fellows and M. A. Langston, On search, decision and the efficiency of polynomial-time algorithms, Proc. 21st ACM Symp. on Theory of Computing, (1989), pp. 501–512.

    Google Scholar 

  19. M. R. Fellows and N. Koblitz, Fixed-parameter complexity and cryptography, Lecture Notes in Computer Science (AAECC10), (1993).

    Google Scholar 

  20. C. H. Papadimitriou and M. Yannakakis, On limited nondeterminism and the complexity of the V-C dimension, Proc. 8th Structure in Complexity Theory Conference, (1993), pp. 12–18.

    Google Scholar 

  21. N. Pippenger and M. J. Fischer, Relations among complexity measures, J. Assoc. Comput. Mach. 26, (1979), pp. 361–381.

    Google Scholar 

  22. J. Plehn and B. Voigt, Finding minimally weighted subgraphs, (1993), to appear.

    Google Scholar 

  23. N. Robertson and P. D. Seymour, Graph minors XV. Wagner's conjecture, to appear.

    Google Scholar 

  24. M. Sipser, Borel sets and circuit complexity, Proc. 15th Ann. ACM Symp. on Theory of Computing, (1983), pp. 61–69.

    Google Scholar 

  25. R. Szelepcsenyi, Î’k-complete problems and greediness, Technique Report # 455, Computer Science Department, University of Rochester, (1993).

    Google Scholar 

  26. M. J. Wolf, Nondeterministic circuits, space complexity, and quasigroups, Theoretical Computer Science, to appear, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cai, L., Chen, J., Downey, R., Fellows, M. (1994). On the structure of parameterized problems in NP. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_167

Download citation

  • DOI: https://doi.org/10.1007/3-540-57785-8_167

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics