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Bookmarks in Grammar-Compressed Strings

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String Processing and Information Retrieval (SPIRE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9954))

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Abstract

We consider the problem of storing a grammar of size n compressing a string of size N, and a set of positions \(\{i_1,\ldots ,i_b\}\) (bookmarks) such that any substring of length l crossing one of the positions can be decompressed in O(l) time. Our solution uses space \(O((n+b)\max \{1,\log ^* n - \log ^*(\frac{n}{b} + \frac{b}{n} )\})\). Existing solutions for the bookmarking problem either require more space or a super-constant “kick-off” time to start the decompression.

P.H. Cording—Supported by the Danish Research Council under the Sapere Aude Program (DFF 4005-00267).

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Notes

  1. 1.

    The bound is in fact \(O(z+b\log ^* N)\), where z is the size of the LZ77 parse of \(S \). Since it is known that \(z\le n' \le n\) [12], where \(n'\) is the size of the smallest SLP generating \(S \), we replace z by n for clarity.

References

  1. Belazzougui, D., Cording, P.H., Puglisi, S.J., Tabei, Y.: Access, rank, and select in grammar-compressed strings. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 142–154. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  2. Belazzougui, D., Gagie, T., Gawrychowski, P., Kärkkäinen, J., Ordónez, A., Puglisi, S.J., Tabei, Y.: Queries on LZ-bounded encodings. In: DCC, pp. 83–92 (2014)

    Google Scholar 

  3. Bille, P., Christiansen, A.R., Cording, P.H., Gørtz, I.L.: Finger search in grammar-compressed strings (2015). CoRR arXiv:1507.02853

  4. Bille, P., Landau, G.M., Raman, R., Sadakane, K., Satti, S.R., Weimann, O.: Random access to grammar-compressed strings and trees. SIAM J. Comput. 44(3), 513–539 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Charikar, M., Lehman, E., Liu, D., Panigrahy, R., Prabhakaran, M., Sahai, A., Shelat, A.: The smallest grammar problem. IEEE Trans. Inf. Theor. 51(7), 2554–2576 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gagie, T., Gawrychowski, P., Kärkkäinen, J., Nekrich, Y., Puglisi, S.J.: LZ77-based self-indexing with faster pattern matching. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 731–742. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Gawrychowski, P.: Faster algorithm for computing the edit distance between SLP-compressed strings. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds.) SPIRE 2012. LNCS, vol. 7608, pp. 229–236. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Knuth, D.E.: Mathematics and computer science: coping with finiteness. Science (New York, NY) 194(4271), 1235–1242 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  9. Larsson, N.J., Moffat, A.: Off-line dictionary-based compression. In: DCC, vol. 88, no. 11, pp. 1722–1732 (2000)

    Google Scholar 

  10. Miyazaki, M., Shinohara, A., Takeda, M.: An improved pattern matching algorithm for strings in terms of straight-line programs. In: Apostolico, A., Hein, J. (eds.) CPM 97. LNCS, vol. 1264, pp. 1–11. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  11. Nevill-Manning, C.G., Witten, I.H.: Identifying hierarchical structure in sequences: a linear-time algorithm. J. Artif. Intell. Res. (JAIR) 7, 67–82 (1997)

    MATH  Google Scholar 

  12. Rytter, W.: Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci. 302(1), 211–222 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Welch, T.A.: A technique for high-performance data compression. Computer 6(17), 8–19 (1984)

    Article  Google Scholar 

  14. Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theor. 23(3), 337–343 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theor. 24(5), 530–536 (1978)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Technical University of Denmark, DTU Compute, Kongens Lyngby, Denmark

    Patrick Hagge Cording

  2. University of Haifa, Haifa, Israel

    Pawel Gawrychowski & Oren Weimann

Authors
  1. Patrick Hagge Cording
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  2. Pawel Gawrychowski
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  3. Oren Weimann
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Correspondence to Patrick Hagge Cording .

Editor information

Editors and Affiliations

  1. Kyushu University , Fukuoka, Japan

    Shunsuke Inenaga

  2. Mathematical Informatics, University of Tokyo , Tokyo, Japan

    Kunihiko Sadakane

  3. Computer Science, Waseda University , Tokyo, Japan

    Tetsuya Sakai

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Cording, P.H., Gawrychowski, P., Weimann, O. (2016). Bookmarks in Grammar-Compressed Strings. In: Inenaga, S., Sadakane, K., Sakai, T. (eds) String Processing and Information Retrieval. SPIRE 2016. Lecture Notes in Computer Science(), vol 9954. Springer, Cham. https://doi.org/10.1007/978-3-319-46049-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-46049-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46048-2

  • Online ISBN: 978-3-319-46049-9

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