International Symposium on String Processing and Information Retrieval

SPIRE 2015: String Processing and Information Retrieval pp 54-66 | Cite as

On Prefix/Suffix-Square Free Words

  • Marius Dumitran
  • Florin Manea
  • Dirk Nowotka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9309)


We present a series of algorithms identifying efficiently the factors of a word that neither start nor end with squares (called, accordingly, prefix-suffix-square free factors). A series of closely related algorithmic problems are discussed.


Linear Time Input Word Free Word Free Factor Random Access Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    García-López, J., Manea, F., Mitrana, V.: Prefix-suffix duplication. J. Comput. Syst. Sci. 80, 1254–1265 (2014)CrossRefMATHGoogle Scholar
  2. 2.
    Chan, S., Blackburn, E.: Telomeres and telomerase. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 359, 109–121 (2004)CrossRefGoogle Scholar
  3. 3.
    Preston, R.: Telomeres, telomerase and chromosome stability. Radiat. Res. 147, 529–534 (1997)CrossRefGoogle Scholar
  4. 4.
    Murnane, J.: Telomere dysfunction and chromosome instability. Mutat. Res. 730, 28–36 (2012)CrossRefGoogle Scholar
  5. 5.
    Lothaire, M.: Combinatorics on Words. Cambridge University Press (1997)Google Scholar
  6. 6.
    Gusfield, D.: Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge University Press, New York (1997)CrossRefMATHGoogle Scholar
  7. 7.
    Xu, Z.: A Minimal Periods Algorithm with Applications. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 51–62. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  8. 8.
    Gawrychowski, P., Manea, F., Nowotka, D.: Testing generalised freeness of words. In: Proc. STACS 2014. LIPIcs, vol. 25, pp. 337–349 (2014)Google Scholar
  9. 9.
    Gabow, H.N., Tarjan, R.E.: A linear-time algorithm for a special case of disjoint set union. In: Proc. STOC, pp. 246–251 (1983)Google Scholar
  10. 10.
    Main, M.G.: Detecting leftmost maximal periodicities. Discrete Appl. Math. 25, 145–153 (1989)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Kolpakov, R., Kucherov, G.: Finding maximal repetitions in a word in linear time. In: Proc. FOCS, pp. 596–604 (1999)Google Scholar
  12. 12.
    Duval, J.-P., Kolpakov, R., Kucherov, G., Lecroq, T., Lefebvre, A.: Linear-Time Computation of Local Periods. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 388–397. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  13. 13.
    Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53, 918–936 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Crochemore, M., Iliopoulos, C.S., Kubica, M., Rytter, W., Waleń, T.: Efficient Algorithms for Two Extensions of LPF Table: The Power of Suffix Arrays. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 296–307. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  15. 15.
    Bender, M.A., Farach-Colton, M.: The LCA problem revisited. In: Gonnet, G., Panario, D., Viola, A., (eds.) LATIN 2000. LNCS, vol. 1776, pp. 88–94. Springer, Heidelberg (2000)Google Scholar
  16. 16.
    Bentley, J.: Decomposable searching problems. Inform. Proc. Letters 8, 244–251 (1979)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Crochemore, M.: An optimal algorithm for computing the repetitions in a word. Inform. Proc. Letters 12, 244–250 (1981)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Department of Computer ScienceChristian-Albrechts University of KielKielGermany

Personalised recommendations