Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7924))

Abstract

We present new θ(n) time algorithms for testing pattern involvement for all length 4 permutations. For most of these permutations the previous best algorithms require O(nlogn) time.

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. Albert, M.H., Aldred, R.E.L., Atkinson, M.D., Holton, D.A.: Algorithms for Pattern Involvement in Permutations. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 355–367. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Berkman, O., Matias, Y., Ragde, P.: Triply-logarithmic parallel upper and lower bounds for minimum and range minima over small domains. Journal of Algorithms 28, 197–215 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berkman, O., Schieber, B., Vishkin, U.: Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. Journal of Algorithms 14, 344–370 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bose, P., Buss, J.F., Lubiw, A.: Pattern matching for permutations. Information Processing Letters 65, 277–283 (1998)

    Article  MathSciNet  Google Scholar 

  5. Fredman, M.L.: On Computing the length of longest increasing subsequences. Discrete Mathematics 11, 29–35 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ibarra, L.: Finding pattern matchings for permutations. Information Processing Letters 61, 293–295 (1997)

    Article  MathSciNet  Google Scholar 

  7. Kitaev, S., Mansour, T.: A survey on certain pattern problems, http://www.ru.is/kennarar/sergey/index_files/Papers/survey.ps , http://ajuarna.staff.gunadarma.ac.id/Downloads/files/1662/survey.pdf

  8. Preparata, F.P., Shamos, M.I.: Computational Geometry, An Introduction. Springer (1985)

    Google Scholar 

  9. Saxena, S.: Dominance made simple. Information Processing Letters 109, 419–421 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tamassia, R., Vitter, J.S.: Optimal cooperative search in fractional cascaded data structures. Algorithmica 15, 154–171 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yugandhar, V., Saxena, S.: Parallel algorithms for separable permutations. Discrete Applied Mathematics 146, 343–364 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Han, Y., Saxena, S. (2013). Algorithms for Testing Length Four Permutations. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38756-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38755-5

  • Online ISBN: 978-3-642-38756-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics