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Longest Gapped Repeats and Palindromes

  • Marius Dumitran
  • Florin ManeaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)

Abstract

A gapped repeat (respectively, palindrome) occurring in a word w is a factor uvu (respectively, \(u^Rvu\)) of w. We show how to compute efficiently, for every position i of the word w, the longest prefix u of w[i..n] such that uv (respectively, \(u^Rv\)) is a suffix of \(w[1..i-1]\) (defining thus a gapped repeat uvu – respectively, palindrome \(u^Rvu\)), and the length of v is subject to various types of restrictions.

Keywords

Linear Time Maximal Repeat Input Word Suffix Array Armed Repeat 
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.

References

  1. 1.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, New York (1997)CrossRefzbMATHGoogle Scholar
  2. 2.
    Brodal, G.S., Lyngsø, R.B., Pedersen, C.N.S., Stoye, J.: Finding maximal pairs with bounded gap. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 134–149. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  3. 3.
    Kolpakov, R.M., Kucherov, G.: Finding repeats with fixed gap. In: Proceedings of SPIRE, pp. 162–168 (2000)Google Scholar
  4. 4.
    Kolpakov, R., Kucherov, G.: Searching for gapped palindromes. Theor. Comput. Sci. 410, 5365–5373 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kolpakov, R., Podolskiy, M., Posypkin, M., Khrapov, N.: Searching of gapped repeats and subrepetitions in a word. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds.) CPM 2014. LNCS, vol. 8486, pp. 212–221. Springer, Heidelberg (2014) Google Scholar
  6. 6.
    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
  7. 7.
    Crochemore, M., Tischler, G.: Computing longest previous non-overlapping factors. Inf. Process. Lett. 111, 291–295 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Crochemore, M., Ilie, L., Iliopoulos, C.S., Kubica, M., Rytter, W., Walen, T.: Computing the longest previous factor. Eur. J. Comb. 34, 15–26 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kolpakov, R., Kucherov, G.: Finding maximal repetitions in a word in linear time. In: Proceedings of FOCS, pp. 596–604 (1999)Google Scholar
  10. 10.
    Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53, 918–936 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gabow, H.N., Tarjan, R.E.: A linear-time algorithm for a special case of disjoint set union. In: Proceeding of STOC, pp. 246–251 (1983)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.
    Kosaraju, S.R.: Computation of squares in a string (preliminary version). In: Crochemore, M., Gusfield, D. (eds.) CPM 1994. LNCS, vol. 807, pp. 146–150. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Crochemore, M., Rytter, W.: Usefulness of the Karp-Miller-Rosenberg algorithm in parallel computations on strings and arrays. Theoret. Comput. Sci. 88, 59–82 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kociumaka, T., Radoszewski, J., Rytter, W., Waleń, T.: Efficient data structures for the factor periodicity problem. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds.) SPIRE 2012. LNCS, vol. 7608, pp. 284–294. Springer, Heidelberg (2012) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

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

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