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Compressed Suffix Array

2003; Grossi, Gupta, Vitter

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Encyclopedia of Algorithms

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Keywords and Synonyms

Compressed full-text indexing; Compressed suffix tree    

Problem Definition

Given a text string \( { T = t_1 t_2 \dots t_n } \) over an alphabet Σ of size σ, the compressed full-text indexing (CFTI) problem asks to create a space-efficient data structure capable of efficiently simulating the functionalities of a full-text index build on T.

A simple example of a full-text index is suffix array \( { A[1,n] } \) that contains a permutation of the interval \( { [1,n] } \), such that \( { T[A[i],n] < T[A[i+1],n] } \) for all \( { 1 \le i < n } \), where “\( { < } \)” between strings is the lexicographical order. Using suffix array, the occurrences of a given pattern \( { P= p_1 p_2 \dots p_m } \) in T can be found using two binary searches in \( { O(m \log n) } \) time.

The CFTI problem related to suffix arrays is easily stated; find a space-efficient data structure supporting the retrieval of value \( { A[i] } \) for any i efficiently. Such a solution is called compressed...

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Notes

  1. 1.

    H k is the minimum average number of bits needed to code one symbol using any compressor that fixes the code word based on the k-symbol context following the the symbol to be coded. See [6] for more formal definition.

  2. 2.

    The description below follows closely the one given in [9]

Recommended Reading

  1. Foschini, L., Grossi, R., Gupta, A., Vitter, J.S.: When indexing equals compression: Experiments with compressing suffix arrays and applications. ACM Trans. Algorithms 2(4), 611–639 (2006)

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  2. Grossi, R., Gupta, A., Vitter, J.: High-order entropy-compressed text indexes. In: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Baltimore, 12–14 January, pp. 841–850 (2003)

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  3. Grossi, R., Vitter, J.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM J. Comput. 35(2), 378–407 (2006)

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  4. Jacobson, G.: Space-efficient static trees and graphs. In: Proc. 30th IEEE Symposium on Foundations of Computer Science (FOCS), Research Triangle Park, 30 October – 1 November, pp. 549–554 (1989)

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  5. Manber, U., Myers, G.: Suffix arrays: a new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)

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  6. Manzini, G.: An analysis of the Burrows-Wheeler transform. J. ACM 48(3), 407–430 (2001)

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  7. Munro, I.: Tables. In: Proc. 16th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS). LNCS, vol. 1180, Hyderabad, 18–20 December, pp. 37–42 (1996)

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  8. Munro, I., Raman, V., Rao, S.: Space efficient suffix trees. J. Algorithms 39(2), 205–222 (2001)

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  9. Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Comput. Surv. 39(1), Article 2 (2007)

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  10. Sadakane, K.: New text indexing functionalities of the compressed suffix arrays. J. Algorithms 48(2), 294–313 (2003)

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  11. Sadakane, K.: Compressed suffix trees with full functionality. Theor. Comput. Syst. 41, 589–607 (2007)

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Helsinki, Helsinki, Finland

    Veli Mäkinen

Authors
  1. Veli Mäkinen
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Mäkinen, V. (2008). Compressed Suffix Array. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_82

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