Skip to main content
SpringerLink
Log in

Completeness Results for Parameterized Space Classes

  • Conference paper
Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

Included in the following conference series:

Abstract

The parameterized complexity of a problem is generally considered “settled” once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have, however, resisted such a classification. At least in some cases, the reason is that upper and lower bounds for their parameterized space complexity have recently been obtained that rule out completeness results for parameterized time classes. In this paper, we make progress in this direction by proving that the associative generability problem and the longest common subsequence problem are complete for parameterized space classes. These classes are defined in terms of different forms of bounded nondeterminism and in terms of simultaneous time–space bounds. As a technical tool we introduce a “union operation” that translates between problems complete for classical complexity classes and for W-classes.

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

Access this chapter

Log in via an institution
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. Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: Advice classes of parameterized tractability. Annals of Pure and Applied Logic 84(1), 119–138 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Elberfeld, M., Stockhusen, C., Tantau, T.: On the Space Complexity of Parameterized Problems. In: Thilikos, D.M., Woeginger, G.J. (eds.) IPEC 2012. LNCS, vol. 7535, pp. 206–217. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Guillemot, S.: Parameterized complexity and approximability of the longest compatible sequence problem. Discrete Optimization 8(1), 50–60 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Flum, J., Grohe, M.: Describing parameterized complexity classes. Information and Computation 187, 291–319 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Stockhusen, C., Tantau, T.: Completeness results for parameterized space classes. Technical Report arXiv:1308.2892, ArXiv e-prints (2013)

    Google Scholar 

  6. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)

    Google Scholar 

  7. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)

    Google Scholar 

  8. Chen, Y., Flum, J., Grohe, M.: Bounded nondeterminism and alternation in parameterized complexity theory. In: Proceedings of the 18th IEEE Annual Conference on Computational Complexity, CCC 2003, pp. 13–29 (2003)

    Google Scholar 

  9. Kintala, C.M.R., Fischer, P.C.: Refining nondeterminism in relativized polynomial-time bounded computations. SIAM Journal on Computing 1(9), 46–53 (1980)

    Article  MathSciNet  Google Scholar 

  10. Buss, J., Goldsmith, J.: Nondeterminism within P. SIAM Journal on Computing, 560–572 (1993)

    Google Scholar 

  11. Buss, S.R.: The Boolean formula value problem is in ALOGTIME. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, STOC 1987, pp. 123–131. ACM (1987)

    Google Scholar 

  12. Buss, S., Cook, S., Gupta, A., Ramachandran, V.: An optimal parallel algorithm for formula evaluation. SIAM Journal on Computing 21(4), 755–780 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jones, N.D., Laaser, W.T.: Complete problems for deterministic polynomial time. Theoretical Computer Science 3(1), 105–117 (1976)

    Article  MathSciNet  Google Scholar 

  14. Jones, N.D., Lien, Y.E., Laaser, W.T.: New problems complete for nondeterministic log space. Mathematical Systems Theory 10(1), 1–17 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: On the parameterized complexity of short computation and factorization. Archive for Mathematical Logic 36(4-5), 321–337 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hartmanis, J.: On non-determinancy in simple computing devices. Acta Informatica 1, 336–344 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fellows, M., Hallett, M., Stege, U.: Analogs & duals of the MAST problem for squences & trees. Journal of Algorithms 49(1), 192–216 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science, Universität zu Lübeck, 23538, Lübeck, Germany

    Christoph Stockhusen & Till Tantau

Authors
  1. Christoph Stockhusen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Till Tantau
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Stockhusen, C., Tantau, T. (2013). Completeness Results for Parameterized Space Classes. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03898-8_28

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation