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Lempel Ziv Computation in Small Space (LZ-CISS)

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Combinatorial Pattern Matching (CPM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

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Abstract

For both the Lempel Ziv 77- and 78-factorization we propose factorization algorithms using \((1+\epsilon ) n \lg n + \mathop {}\mathopen {}\mathcal {O}\mathopen {}\left( n\right) \) bits (for any positive constant \(\epsilon \le 1\)) working space (including the space for the output) for any text of size \(n\) over an integer alphabet in \(\mathop {}\mathopen {}\mathcal {O}\mathopen {}\left( n / \epsilon ^{2}\right) \) time.

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References

  1. Amir, A., Farach, M., Idury, R.M., Poutré, J.A.L., Schäffer, A.A.: Improved dynamic dictionary matching. Inf. Comput. 119(2), 258–282 (1995)

    Article  MATH  Google Scholar 

  2. Bannai, H., Inenaga, S., Takeda, M.: Efficient LZ78 factorization of grammar compressed text. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds.) SPIRE 2012. LNCS, vol. 7608, pp. 86–98. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Benoit, D., Demaine, E.D., Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Representing trees of higher degree. Algorithmica 43(4), 275–292 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fischer, J., I, T., Köppl, D.: Lempel Ziv computation in small space (LZ-CISS) (2015). arXiv:1504.02605

  5. Fischer, J.: Optimal succinctness for range minimum queries. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 158–169. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Fischer, J., Gawrychowski, P.: Alphabet-dependent string searching with wexponential search trees. In: Cicalese, F., Porat, E., Vaccaro, U. (eds.) CPM 2015. LNCS, vol. 9133, pp. 160–171. Springer, Heidelberg (2015)

    Google Scholar 

  7. Goto, K., Bannai, H.: Simpler and faster Lempel Ziv factorization. In: Proceedings of the 2013 Data Compression Conference, DCC 2013, pp. 133–142. IEEE Computer Society, Washington (2013)

    Google Scholar 

  8. Goto, K., Bannai, H.: Space efficient linear time Lempel-Ziv factorization for small alphabets. In: Data Compression Conference, DCC 2014, Snowbird, UT, USA, 26–28 March 2014, pp. 163–172 (2014)

    Google Scholar 

  9. Jansson, J., Sadakane, K., Sung, W.: Linked dynamic tries with applications to LZ-compression in sublinear time and space. Algorithmica 71(4), 969–988 (2015)

    Article  MathSciNet  Google Scholar 

  10. Kärkkäinen, J., Kempa, D., Puglisi, S.J.: Linear time Lempel-Ziv factorization: simple, fast, small. In: Fischer, J., Sanders, P. (eds.) CPM 2013. LNCS, vol. 7922, pp. 189–200. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53(6), 918–936 (2006)

    Article  MathSciNet  Google Scholar 

  12. Kempa, D., Puglisi, S.J.: Lempel-Ziv factorization: simple, fast, practical. In: ALENEX, pp. 103–112 (2013)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Succinct representations of permutations and functions. Theor. Comput. Sci. 438, 74–88 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Nakashima, Y., I, T., Inenaga, S., Bannai, H., Takeda, M.: Constructing LZ78 tries and position heaps in linear time for large alphabets. Inform. Process. Lett. 115(9), 655–659 (2015)

    Article  MathSciNet  Google Scholar 

  16. Navarro, G., Sadakane, K.: Fully functional static and dynamic succinct trees. ACM Trans. Algorithms 10(3), 16:1–16:39 (2014)

    Article  MathSciNet  Google Scholar 

  17. Ohlebusch, E., Fischer, J., Gog, S.: CST++. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 322–333. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Välimäki, N., Mäkinen, V., Gerlach, W., Dixit, K.: Engineering a compressed suffix tree implementation. ACM J. Exp. Algorithmics 14 (2009)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, TU Dortmund, Dortmund, Germany

    Johannes Fischer, Tomohiro I & Dominik Köppl

Authors
  1. Johannes Fischer
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  2. Tomohiro I
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  3. Dominik Köppl
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Corresponding author

Correspondence to Dominik Köppl .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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Fischer, J., I, T., Köppl, D. (2015). Lempel Ziv Computation in Small Space (LZ-CISS). In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

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