Skip to main content
SpringerLink
Log in

Some New Directions and Questions in Parameterized Complexity

  • Conference paper
Developments in Language Theory (DLT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3340))

Included in the following conference series:

  • 509 Accesses

Abstract

Recently there have been some new initiatives in the field of parameterized complexity. In this paper, we will report on some of these, concentrating on some open questions, and also looking at some current investigations aimed towards applying ideas of parameterized complexity in the field of online model theory.

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. Abrahamson, K., Downey, R., Fellows, M.: Fixed Parameter Tractability and Completeness IV: On Completeness for W[P] and PSPACE Analogs. Annals of Pure and Applied Logic 73, 235–276 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  3. Alekhnovich, M., Razborov, A.: Resolution is Not Automatizable Unless W[P] is Tractable. In: Proc. of the 42nd IEEE FOCS, pp. 210–219 (2001)

    Google Scholar 

  4. Arora, S.: Polynomial Time Approximation Schemes for Euclidean TSP and Other Geometric Problems. In: Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, pp. 2–12 (1996)

    Google Scholar 

  5. Arora, S.: Nearly Linear Time Approximation Schemes for Euclidean TSP and Other Geometric Problems. In: Proc. 38th Annual IEEE Symposium on the Foundations of Computing (FOCS 1997), pp. 554–563. IEEE Press, Los Alamitos (1997)

    Chapter  Google Scholar 

  6. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof Verification and Intractability of Approximation Algorithms. In: Proceedings of the IEEE Symposium on the Foundations of Computer Science (1992)

    Google Scholar 

  7. Bazgan, C.: Schémas d’approximation et complexité paramétrée, Rapport de stage de DEA d’Informatique à Orsay (1995)

    Google Scholar 

  8. Cai, L., Chen, J.: On Fixed-Parameter Tractability and Approximability of NP-Hard Optimization Problems. J. Computer and Systems Sciences 54, 465–474 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cai, L., Fellows, M., Juedes, D., Rosamond, F.: Efficient Polynomial-Time Approximation Schemes for Problems on Planar Stru ctures: Upper and Lower Bounds, manuscript (2001)

    Google Scholar 

  10. Cai, L., Juedes, D.: On the existence of subexponential time parameterized algorithms. J. Comput. Sys. Sci. 67, 789–807 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chekuri, C., Khanna, S.: A PTAS for the Multiple Knapsack Problem. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), pp. 213–222 (2000)

    Google Scholar 

  12. Chen, J., Kanj, I.A., Jia, W.: Vertex Cover: Further Observations and Further Improvements. Journal of Algorithms 41, 280–301 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen, J., Huang, X., Kanj, I.A., Xia, G.: Polynomial time approximation schemes and parameterized complexity. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 500–512. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Chen, J., Miranda, A.: A Polynomial-Time Approximation Scheme for General Multiprocessor Scheduling. In: Proc. ACM Symposium on Theory of Computing (STOC 1999), pp. 418–427. ACM Press, New York (1999)

    Chapter  Google Scholar 

  15. Chrobak, M., Slusarek, M.: On some packing problems related to dynamic storage allogation. RARIO Inform. Theor. Appl. 22, 487–499 (1988)

    MATH  MathSciNet  Google Scholar 

  16. Downey, R.: Parameterized complexity for the skeptic. In: Proceeding of the 18th Annual IEEE Conference on Comutational Complexity (2003)

    Google Scholar 

  17. Downey, R., Estivill-Castro, V., Fellows, M., Prieto-Rodriguez, E., Rosamond, F.: Cutting Up Is Hard To Do: the Parameterized Complexity of k-Cut and Related Problems. In: Proc. Australian Theory Symposium, CATS (2003)

    Google Scholar 

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

    Google Scholar 

  19. Downey, R.G., McCartin, C.: Online problems, pathwidth, and persistence. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 13–24. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Downey, R.G., McCartin, C.M.: Bounded Persistence Pathwidth (to appear)

    Google Scholar 

  21. Erlebach, T., Jansen, K., Seidel, E.: Polynomial Time Approximation Schemes for Geometric Graphs. In: Proc. ACM Symposium on Discrete Algorithms (SODA 2001), pp. 671–679 (2001)

    Google Scholar 

  22. Fellows, M.: Parameterized complexity: the main ideas and connections to practical computing. In: Fleischer, R., Moret, B.M.E., Schmidt, E.M. (eds.) Experimental Algorithmics. LNCS, vol. 2547, pp. 51–77. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Fellows, M.: Personal communication (March 2003)

    Google Scholar 

  24. Flum, J., Grohe, M.: Parameterized complexity and subexponential time. In: Bulletin EATCS (to appear)

    Google Scholar 

  25. Flum, J., Grohe, M., Weyer, M.: Bounded fixed-parameter tractability and log2 nondeterministic bits. Journal of Comput. Sys. Sci. (to appear)

    Google Scholar 

  26. Frick, M., Grohe, M.: The Complexity of First-Order and Monadic Second-Order Logic Revisited. In: LICS, pp. 215–224 (2002)

    Google Scholar 

  27. Fouhy, J.: Computational Experiments on Graph Width Metrics, MSc Thesis, Victoria University, Wellington (2003)

    Google Scholar 

  28. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  29. Impagliazzo, R., Paturi, R.: On the complexity of K-SAT. JCSS 62(2), 367–375 (2001)

    MATH  MathSciNet  Google Scholar 

  30. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? JCSS 63(4), 512–530 (2001)

    MATH  MathSciNet  Google Scholar 

  31. Irani, S.: Coloring Inductive Graphs On-Line. Algorithmica 11, 53–72 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  32. Khanna, S., Motwani, R.: Towards a Syntactic Characterization of PTAS. In: Proc. STOC 1996, pp. 329–337. ACM Press, New York (1996)

    Google Scholar 

  33. Kierstead, H.A.: The Linearity of First Fit Coloring of Interval Graphs. SIAM J. on Discrete MAth 1(4), 526–530 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  34. Kierstead, H., Qin, J.: Colouring interval graphs with First-Fit. Discrete Math 144, 47–57 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  35. Kierstead, H., Trotter, W.: The linearity of first-fit colouring of interval graphs. SIAM J. on Discrete Math. 1, 528–530 (1988)

    Google Scholar 

  36. McCartin, C.: Contributions to Parameterized Complexity, PhD Thesis, Victoria University, Wellington (2003)

    Google Scholar 

  37. Niedermeier, R.: Ubiquitous parameterization — invitation to fixed-parameter algorithms. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 84–103. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  38. Niedermeier, R.: Fixed Parameter Algorithms. Oxford University Press, Oxford (in preparation)

    Google Scholar 

  39. Rubin, S.: Automatic Structures, PhD Diss, Auckland University (2004)

    Google Scholar 

  40. Shamir, R., Tzur, D.: The Maximum Subforest Problem: Approximation and Exact Algorithms. In: Proc. ACM Symposium on Discrete Algorithms (SODA 1998), pp. 394–399. ACM Press, New York (1998)

    Google Scholar 

  41. Stege, U.: Resolving Conflicts in Problems in Computational Biochemistry, Ph.D. dissertation, ETH (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Victoria University, Wellington, New Zealand

    Rodney G. Downey

  2. Massey University, Palmerston North, New Zealand

    Catherine McCartin

Authors
  1. Rodney G. Downey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Catherine McCartin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude

  2. Computer Science, Institute of Information and Mathematical Sciences, Massey University Albany, Auckland, New Zealand

    Elena Calude

  3. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Michael J. Dinneen

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Downey, R.G., McCartin, C. (2004). Some New Directions and Questions in Parameterized Complexity. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30550-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24014-3

  • Online ISBN: 978-3-540-30550-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation