Skip to main content
SpringerLink
Log in

Reporting Consecutive Substring Occurrences Under Bounded Gap Constraints

  • Conference paper
  • First Online:
Combinatorial Pattern Matching (CPM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

Included in the following conference series:

  • 815 Accesses

Abstract

We study the problem of indexing a text \(T[1\dots n]\) such that whenever a pattern \(P[1\dots p]\) and an interval \([\alpha , \beta ]\) comes as a query, we can report all pairs \((i, j)\) of consecutive occurrences of \(P\) in \(T\) with \(\alpha \le j-i \le \beta \). We present an \(O(n\log n)\) space data structure with optimal \(O(p+k)\) query time, where \(k\) is the output size.

G. Navarro—Funded with Basal Funds FB0001, Conicyt, Chile.

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 EPUB and 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

Notes

  1. 1.

    This is optimal in the RAM model if we assume a general alphabet of size \(O(n)\).

References

  1. Gusfield, D.: Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press, New York (1997)

    Book  MATH  Google Scholar 

  2. Aluru, S. (ed.): Handbook of Computational Molecular Biology. CRC Computer and Information Science Series. Chapman and Hall, London (2005)

    Google Scholar 

  3. Ohlebusch, E.: Bioinformatics Algorithms: Sequence Analysis, Genome Rearrangements, and Phylogenetic Reconstruction. Oldenbusch Verlag, Bremen (2013)

    Google Scholar 

  4. Iliopoulos, C.S., Rahman, M.S.: Indexing factors with gaps. Algorithmica 55, 60–70 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bille, P., Gørtz, I.L.: Substring range reporting. Algorithmica 69, 384–396 (2014)

    Article  MathSciNet  Google Scholar 

  6. Bille, P., Gørtz, I.L., Vildhøj, H.W., Vind, S.: String indexing for patterns with wildcards. Theor. Comput. Syst. 55, 41–60 (2014)

    Article  MATH  Google Scholar 

  7. Keller, O., Kopelowitz, T., Lewenstein, M.: Range non-overlapping indexing and successive list indexing. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 625–636. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Muthukrishnan, S.: Efficient algorithms for document retrieval problems. In: Proceedings of 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 657–666 (2002)

    Google Scholar 

  9. Brodal, G.S., Lyngsø, R.B., Pedersen, C.N.S., Stoye, J.: Finding maximal pairs with bounded gap. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 134–149. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Weiner, P.: Linear pattern matching algorithms. In: 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, 15–17 October, pp. 1–11 (1973)

    Google Scholar 

  11. Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26, 362–391 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tao, Y.: Dynamic ray stabbing. ACM Trans. Algorithms 11, 11 (2014)

    Article  MathSciNet  Google Scholar 

  13. Alstrup, S., Brodal, G.S., Rauhe, T.: Optimal static range reporting in one dimension. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, Heraklion, Crete, Greece, 6–8 July, pp. 476–482 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Biotechnology and Bioengineering, Department of Computer Science, University of Chile, Santiago, Chile

    Gonzalo Navarro

  2. School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, USA

    Sharma V. Thankachan

Authors
  1. Gonzalo Navarro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sharma V. Thankachan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gonzalo Navarro .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Navarro, G., Thankachan, S.V. (2015). Reporting Consecutive Substring Occurrences Under Bounded Gap Constraints. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19929-0_31

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation