Efficient Algorithm for Circular Burrows-Wheeler Transform

  • Wing-Kai Hon
  • Tsung-Han Ku
  • Chen-Hua Lu
  • Rahul Shah
  • Sharma V. Thankachan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)

Abstract

Given a set \({\cal P}\) of d patterns, the circular dictionary matching problem is to index \({\cal P}\) such that for any online query text T, we can quickly locate the occurrences of any cyclic shift of any pattern of \({\cal P}\) within T efficiently. This problem can be applied on practical problems that arise in bioinformatics and computational geometry. Recently, Hon et al. (2011) applied a variant of the well-known Burrows-Wheeler transform, called circular Burrows-Wheeler transform (circular BWT) [Mantaci, Restivo, Rosone, and Sciortino, Theoretical Computer Science, 2007], and showed that this can be used to solve the circular dictionary matching problem efficiently. In this paper, we give the first construction algorithm for the circular BWT, which takes O(nlogn) time and requires O(nlogσ) bits working space, where n denotes the total length of the patterns in \({\cal P}\) and σ is the alphabet size.

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References

  1. 1.
    Aho, A., Corasick, M.: Efficient String Matching: An Aid to Bibligoraphic Search. Communications of the ACM 18(6), 333–340 (1975)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Belazzougui, D.: Succinct Dictionary Matching with No Slowdown. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 88–100. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Burrows, M., Wheeler, D.J.: A Block-sorting Lossless Data Compression Algorithm. Technical Report 124, Digital Equipment Corporation, Paolo Alto, CA, USA (1994)Google Scholar
  4. 4.
    Chan, H.L., Hon, W.K., Lam, T.W., Sadakane, K.: Compressed Indexes for Dynamic Text Collections. ACM Transactions on Algorithms 3(2) (2007)Google Scholar
  5. 5.
    Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, New York (1994)MATHGoogle Scholar
  6. 6.
    Eisen, J.A.: Environmental Shotgun Sequencing: Its Potential and Challenges for Studying the Hidden World of Microbes. PLoS Biology 5(3), e82 (2007)Google Scholar
  7. 7.
    Hon, W.-K., Lu, C.-H., Shah, R., Thankachan, S.V.: Succinct Indexes for Circular Patterns. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 673–682. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Hon, W.-K., Ku, T.-H., Shah, R., Thankachan, S.V., Vitter, J.S.: Faster Compressed Dictionary Matching. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 191–200. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Hon, W.K., Lam, T.W., Sadakane, K., Sung, W.K., Yiu, S.M.: A Space and Time Efficient Algorithm for Constructing Compressed Suffix Arrays. Algorithmica 48(1), 28–36 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hon, W.K., Lam, T.W., Shah, R., Tam, S.L., Vitter, J.S.: Compressed Index for Dictionary Matching. In: DCC, pp. 23–32 (2008)Google Scholar
  11. 11.
    Hon, W.K., Sadakane, K., Sung, W.K.: Breaking a Time-and-Space Barrier in Constructing Full-Text Indices. SIAM J. Computing 38(6), 2162–2178 (2009)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Iliopoulos, C.S., Rahman, M.S.: Indexing Circular Patterns. In: Nakano, S.-I., Rahman, M.S. (eds.) WALCOM 2008. LNCS, vol. 4921, pp. 46–57. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Larsson, N.J., Sadakane, K.: Faster suffix sorting. Theoretical Computer Science 387(3), 258–272 (2007)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Mantaci, S., Restivo, A., Rosone, G., Sciortino, M.: An Extension of the Burrows Wheeler Transform. Theoretical Computer Science 387(3), 298–312 (2007)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Raman, R., Raman, V., Rao, S.S.: Succinct Indexable Dictionaries with Applications to Encoding k-ary Trees and Multisets. In: SODA, pp. 233–242 (2002)Google Scholar
  16. 16.
    Simon, C., Daniel, R.: Metagenomic Analyses: Past and Future Trends. Applied and Environmental Microbiology 77(4), 1153–1161 (2011)CrossRefGoogle Scholar
  17. 17.
    Strang, B.L., Stow, N.D.: Circularization of the Herpes Simplex Virus Type 1 Genome upon Lytic Infection. Journal of Virology 79(19), 12487–12494 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wing-Kai Hon
    • 1
  • Tsung-Han Ku
    • 1
  • Chen-Hua Lu
    • 2
  • Rahul Shah
    • 3
  • Sharma V. Thankachan
    • 3
  1. 1.National Tsing Hua UniversityTaiwan
  2. 2.Academia SinicaTaiwan
  3. 3.Louisiana State UniversityUSA

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