skip to main content
article

Computing Longest Previous non-overlapping Factors

Published: 01 February 2011 Publication History

Abstract

The Longest Previous non-overlapping Factor table (LPnF) stores for each position of a string the maximal length of factors occurring both there and in the preceding part of the string. The notion is a slight variant of the LPF table described before and used for text compression. The LPnF table is an essential element for the design of efficient algorithms on strings as it is related to a certain type of Ziv-Lempel factorisation used for this purpose. We show how to compute the LPnF table in linear time from the suffix array of the string when it is drawn from an integer alphabet. The algorithm is a non-immediate extension of the LPF computation and it does not require any other sophisticated data structure than the suffix array of the input string.

References

[1]
Berstel, J. and Savelli, A., Crochemore factorization of Sturmian and other infinite words. In: Kralovic, R., Urzyczyn, P. (Eds.), LNCS, vol. 4162. Springer. pp. 157-166.
[2]
Crochemore, M., Transducers and repetitions. Theoretical Computer Science. v45 i1. 63-86.
[3]
Crochemore, M., Hancart, C. and Lecroq, T., Algorithms on Strings. 2007. Cambridge University Press, Cambridge, UK.
[4]
Crochemore, M. and Ilie, L., Computing longest previous factor in linear time and applications. Inf. Process. Lett. v106 i2. 75-80.
[5]
Crochemore, M., Ilie, L., Iliopoulos, C., Kubica, M., Rytter, W. and Waleń, T., LPF computation revisited. In: Fronçek, D., Kratochvíl, J., Miller, M. (Eds.), LNCS, vol. 5874. Springer. pp. 158-169.
[6]
Crochemore, M., Iliopoulos, C., Kubica, M., Rytter, W. and Waleń, T., Efficient algorithms for two extensions of the LPF table: the power of Suffix Arrays. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (Eds.), LNCS, vol. 5901. Springer, Berlin. pp. 296-307.
[7]
Franek, F., Holub, J., Smyth, W.F. and Xiao, X., Computing quasi suffix arrays. Journal of Automata, Languages and Combinatorics. v8 i4. 593-606.
[8]
Kärkkäinen, J., Manzini, G. and Puglisi, S.J., Permuted longest-common-prefix array. In: Kucherov, G., Ukkonen, E. (Eds.), LNCS, vol. 5577. Springer. pp. 181-192.
[9]
Kasai, T., Lee, G., Arimura, H., Arikawa, S. and Park, K., Linear-time longest-common-prefix computation in suffix arrays and its applications. In: LNCS, vol. 2089. Springer. pp. 181-192.
[10]
R.M. Kolpakov, G. Kucherov, Finding maximal repetitions in a word in linear time, in: Foundations of Computer Science, 1999, pp. 596-604.
[11]
Main, M.G., Detecting leftmost maximal periodicities. Discrete Appl. Math. v25. 145-153.
[12]
Ziv, J. and Lempel, A., A universal algorithm for sequential data compression. IEEE Transactions on Information Theory. v23 i3. 337-343.

Cited By

View all
  1. Computing Longest Previous non-overlapping Factors

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image Information Processing Letters
    Information Processing Letters  Volume 111, Issue 6
    February, 2011
    51 pages

    Publisher

    Elsevier North-Holland, Inc.

    United States

    Publication History

    Published: 01 February 2011

    Author Tags

    1. Design of algorithms
    2. Detection of repetitions
    3. Longest previous factor
    4. Suffix array
    5. Text compression
    6. Ziv-Lempel factorisation

    Qualifiers

    • Article

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)0
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 20 Jan 2025

    Other Metrics

    Citations

    Cited By

    View all

    View Options

    View options

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media