Skip to main content
SpringerLink
Log in

Efficient Indexes for the Positional Pattern Matching Problem and Two Related Problems over Small Alphabets

  • Conference paper
Algorithms and Computation (ISAAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6507))

Included in the following conference series:

Abstract

In this paper, we study the following three variants of the classical text indexing problem over small alphabets: the positional pattern matching problem, the position-restricted pattern matching problem, and the indexing version of the variable-length don’t care pattern matching problem. Let n be the length of the text, p be the length of a query pattern, and Σ be the alphabet. Assume that |Σ| = O(polylog(n)). For the first and third problems, we present O(n)-word indexes with O(p) query time. For the second problem, we show that each query can be answered in O(n logε n) space and O(p + occ) time, or in O(n) space and O(p + occ logε n) time, where occ is the number of outputs. When the alphabet size is O(polylog(n)), the indexes presented in this paper improve the results in [6, 10, 11, 22].

This research is supported by the National Science Council of the Republic of China under grant NSC-98-2221-E-007-081.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.00
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. Bentley, J.L.: Solutions to Klee’s rectangle problems. Department of Computer Science, Carnegie Mellon University (1977) (manuscript)

    Google Scholar 

  2. Bertossi, A.A., Lodi, E.: Parallel string matching with variable length don’t cares. J. Parallel Distrib. Comput. 22(2), 229–234 (1994)

    Article  MATH  Google Scholar 

  3. Brodal, G.S., Jørgensen, A.G.: Data structures for range median queries. In: Dong, Y., Du, D.-Z., Ibarra, O.H. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 822–831. Springer, Heidelberg (2009)

    Google Scholar 

  4. Chazelle, B.: A functional approach to data structures and its use in multidimensional searching. SIAM J. Comput. 17(3), 427–462 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  5. Clark, D.: Compact pat trees. PhD Thesis, Univ. Waterloo (1996)

    Google Scholar 

  6. Crochemore, M., Iliopoulos, C.S., Kubica, M., Rahman, M.S., Walen, T.: Improved algorithms for the range next value problem and applications. In: 25th Annual Symposium on Theoretical Aspects of Computer Science, pp. 205–216 (2008)

    Google Scholar 

  7. Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Transactions on Algorithms 3(2) (2007)

    Google Scholar 

  8. Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compressed text indexes. In: 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 841–850 (2003)

    Google Scholar 

  9. Hagerup, T., Miltersen, P.B., Pagh, R.: Deterministic dictionaries. J. Algorithms 41(1), 69–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Inenaga, S., Takeda, M., Shinohara, A., Hoshino, H., Arikawa, S.: The minimum DAWG for all suffixes of a string and its applications. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 153–167. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. 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 

  12. Kucherov, G., Rusinowitch, M.: Matching a set of strings with variable length don’t cares. Theor. Comput. Sci. 178(1-2), 129–154 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lam, T.-W., Sung, W.-K., Tam, S.-L., Yiu, S.-M.: Space efficient indexes for string matching with don’t cares. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 846–857. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Mäkinen, V., Navarro, G.: Rank and Select Revisited and Extended. Theor. Comput. Sci. 387(3), 332–347 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. McCreight, E.M.: A space-economical suffix tree construction algorithm. J. ACM 23(2), 262–272 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  16. Munro, J.I.: Tables. In: 16th Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 37–42 (1996)

    Google Scholar 

  17. Pinter, R.Y.: Efficient string matching with don’t-cares. Combinatorial Algorithms on Words 12, 11–29 (1985)

    Article  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  19. Sustik, M.A., Moore, J.S.: String searching over small alphabets. Technical Report TR-07-62, Department of Computer Sciences, University of Texas at Austin (2007)

    Google Scholar 

  20. Thathoo, R., Virmani, A., Lakshmi, S.S., Balakrishnan, N., Sekar, K.: TVSBS: A fast exact pattern matching algorithm for biological sequences. Current Sciences 91(1), 47–53 (2006)

    Google Scholar 

  21. Willard, D.E.: Examining computational geometry, van Emde Boas trees, and hashing from the perspective of the fusion tree. SIAM J. Comput. 29(3), 1030–1049 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yu, C.-C., Hon, W.-K., Wang, B.-F.: Efficient data structures for the orthogonal range successor problem. In: Ngo, H.Q. (ed.) COCOON 2009. LNCS, vol. 5609, pp. 96–105. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, National Tsing Hua University, Hsinchu, 30013, Taiwan, Republic of China

    Chih-Chiang Yu, Biing-Feng Wang & Chung-Chin Kuo

Authors
  1. Chih-Chiang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Biing-Feng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chung-Chin Kuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, Yuseong-gu, 305-701, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yu, CC., Wang, BF., Kuo, CC. (2010). Efficient Indexes for the Positional Pattern Matching Problem and Two Related Problems over Small Alphabets. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17514-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17513-8

  • Online ISBN: 978-3-642-17514-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation