Skip to main content

Algorithms for Jumbled Indexing, Jumbled Border and Jumbled Square on Run-Length Encoded Strings

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8799))

Abstract

Jumbled Indexing, the problem of indexing a text for histogram queries, has been of much interest lately. In this paper we consider jumbled indexing for run-length encoded texts. We refute a former conjecture and show an algorithm for general sized alphabets. We also consider Jumbled Borders, the extension of borders to jumbled strings. Borders are the basis for various algorithms. Finally, we consider Jumbled Squares, strings which are of the form \(x\bar{x}\), where \(\bar{x}\) is a jumbling of x. We show efficient algorithms for these problems.

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. Amir, A., Butman, A., Porat, E.: On the relationship between histogram indexing and block-mass indexing. Philosophical Transactions A (to appear)

    Google Scholar 

  2. Amir, A., Chan, T.M., Lewenstein, M., Lewenstein, N.: On hardness of jumbled indexing. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 114–125. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Badkobeh, G., Fici, G., Kroon, S., Lipták, Z.: Binary jumbled string matching for highly run-length compressible texts. Information Processing Letters 113(17), 604–608 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benson, G.: Composition alignment. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 447–461. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Böcker, S.: Simulating multiplexed snp discovery rates using base-specific cleavage and mass spectrometry. Bioinformatics 23(2), 5–12 (2007)

    Article  Google Scholar 

  6. Burcsi, P., Cicalese, F., Fici, G., Lipták, Z.: On table arrangements, scrabble freaks, and jumbled pattern matching. In: Boldi, P. (ed.) FUN 2010. LNCS, vol. 6099, pp. 89–101. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Burcsi, P., Cicalese, F., Fici, G., Lipták, Z.: Algorithms for jumbled pattern matching in strings. International Journal of Foundations of Computer Science 23(02), 357–374 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Burcsi, P., Cicalese, F., Fici, G., Lipták, Z.: On approximate jumbled pattern matching in strings. Theory of Computing Systems 50(1), 35–51 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chazelle, B.: Filtering search: A new approach to query-answering. SIAM Journal on Computing 15(3), 703–724 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cicalese, F., Fici, G., Lipták, Z.: Searching for jumbled patterns in strings. In: Proceedings of the Prague Stringology Conference, pp. 105–117 (2009)

    Google Scholar 

  11. Cicalese, F., Gagie, T., Giaquinta, E., Laber, E.S., Lipták, Z., Rizzi, R., Tomescu, A.I.: Indexes for jumbled pattern matching in strings, trees and graphs. In: Kurland, O., Lewenstein, M., Porat, E. (eds.) SPIRE 2013. LNCS, vol. 8214, pp. 56–63. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Durocher, S., Munro, J.I., Mondal, D., Thankachan, S.V.: Jumbled pattern matching over large alphabets. Manuscript, Personal Communication (2014)

    Google Scholar 

  13. Eres, R., Landau, M.G., Parida, L.: Permutation pattern discovery in biosequences. Journal of Computational Biology 11(6), 1050–1060 (2004)

    Article  Google Scholar 

  14. Gagie, T.: Grammar-based construction of indexes for binary jumbled pattern matching. CoRR, abs/1210.8386 (2012)

    Google Scholar 

  15. Gagie, T., Hermelin, D., Landau, G.M., Weimann, O.: Binary jumbled pattern matching on trees and tree-like structures. CoRR, abs/1301.6127 (2013)

    Google Scholar 

  16. Giaquinta, E., Grabowski, S.: New algorithms for binary jumbled pattern matching. Information Processing Letters 113(14-16), 538–542 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hermelin, D., Landau, G.M., Rabinovich, Y., Weimann, O.: Binary jumbled pattern matching via all-pairs shortest paths. CoRR, abs/1401.2065 (2014)

    Google Scholar 

  18. Kociumaka, T., Radoszewski, J., Rytter, W.: Efficient indexes for jumbled pattern matching with constant-sized alphabet. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 625–636. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Lacroix, V., Fernandes, C.G., Sagot, M.-F.: Motif search in graphs: Application to metabolic networks. IEEE/ACM Trans. Comput. Biology Bioinform. 3(4), 360–368 (2006)

    Article  Google Scholar 

  20. Moosa, T.M.: Rahman M. S. Indexing permutations for binary strings. Information Processing Letters 110(18-19), 795–798 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Moosa, T.M., Rahman, M.S.: Sub-quadratic time and linear space data structures for permutation matching in binary strings. Journal of Discrete Algorithms 10, 5–9 (2012)

    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

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Amir, A., Apostolico, A., Hirst, T., Landau, G.M., Lewenstein, N., Rozenberg, L. (2014). Algorithms for Jumbled Indexing, Jumbled Border and Jumbled Square on Run-Length Encoded Strings. In: Moura, E., Crochemore, M. (eds) String Processing and Information Retrieval. SPIRE 2014. Lecture Notes in Computer Science, vol 8799. Springer, Cham. https://doi.org/10.1007/978-3-319-11918-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11918-2_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11917-5

  • Online ISBN: 978-3-319-11918-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics