Skip to main content

A Filtering Algorithm for k-Mismatch with Don’t Cares

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4726))

Abstract

We present a filtering based algorithm for the k-mismatch pattern matching problem with don’t cares. Given a text t of length n and a pattern p of length m with don’t care symbols in either p or t and a bound k, our algorithm finds all the places that the pattern matches the text with at most k mismatches. The algorithm is deterministic and runs in O(nm 1/3 k 1/3log2/3 m) time. The location of the mismatches at each alignment is also given at no extra cost.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abrahamson, K.: Generalized string matching. SIAM journal on Computing 16(6), 1039–1051 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Akutsu, T.: Approximate string matching with don’t care characters. Information Procesing Letters 55, 235–239 (1995)

    Article  MathSciNet  Google Scholar 

  3. Amir, A., Lewenstein, M., Porat, E.: Faster algorithms for string matching with k mismatches. J. Algorithms 50(2), 257–275 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boyer, R.S., Moore, J.S.: A fast string matching algorithm. Communications of the ACM 20, 762–772 (1977)

    Article  Google Scholar 

  5. Clifford, P., Clifford, R.: Simple deterministic wildcard matching. Information Processing Letters 101(2), 53–54 (2007)

    Article  MathSciNet  Google Scholar 

  6. Cole, R., Hariharan, R.: Verifying candidate matches in sparse and wildcard matching. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 592–601. ACM Press, New York (2002)

    Google Scholar 

  7. Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)

    Google Scholar 

  8. Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  9. Fischer, M., Paterson, M.: String matching and other products. In: Karp, R. (ed.) Proceedings of the 7th SIAM-AMS Complexity of Computation, pp. 113–125 (1974)

    Google Scholar 

  10. Indyk, P.: Faster algorithms for string matching problems: Matching the convolution bound. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, pp. 166–173 (1998)

    Google Scholar 

  11. Kalai, A.: Efficient pattern-matching with don’t cares. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 655–656, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics (2002)

    Google Scholar 

  12. Knuth, D.E., Morris, J.H., Pratt, V.B.: Fast pattern matching in strings. SIAM Journal of Computing 6, 323–350 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kosaraju, S.R.: Efficient string matching. Manuscript (1987)

    Google Scholar 

  14. Landau, G.M., Vishkin, U.: Efficient string matching with k mismatches. Theoretical Computer Science 43, 239–249 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Landau, G.M., Vishkin, U.: Efficient string matching in the presence of errors. In: Proc. 26th IEEE FOCS, p. 126 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Nivio Ziviani Ricardo Baeza-Yates

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Clifford, R., Porat, E. (2007). A Filtering Algorithm for k-Mismatch with Don’t Cares. In: Ziviani, N., Baeza-Yates, R. (eds) String Processing and Information Retrieval. SPIRE 2007. Lecture Notes in Computer Science, vol 4726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75530-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75530-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75529-6

  • Online ISBN: 978-3-540-75530-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics