Advertisement

Block Palindromes: A New Generalization of Palindromes

  • Keisuke GotoEmail author
  • I Tomohiro
  • Hideo Bannai
  • Shunsuke Inenaga
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11147)

Abstract

We study a new generalization of palindromes and gapped palindromes called block palindromes. A block palindrome is a string that becomes a palindrome when identical substrings are replaced with a distinct character. We investigate several properties of block palindromes and in particular, study substrings of a string which are block palindromes. In so doing, we introduce the notion of a maximal block palindrome, which leads to a compact representation of all block palindromes that occur in a string. We also propose an algorithm which enumerates all maximal block palindromes that appear in a given string \(T\) in \(O(|T| + \Vert MBP (T)\Vert )\) time, where \(\Vert MBP (T)\Vert \) is the output size, which is optimal unless all the maximal block palindromes can be represented in a more compact way.

Keywords

Palindrome Enumeration algorithm Factorization 

References

  1. 1.
    The 2015 British Informatics Olympiad (2015). http://olympiad.org.uk/2015/index.html. Accessed 13 June 2018
  2. 2.
    Alatabbi, A., Iliopoulos, C.S., Rahman, M.S.: Maximal palindromic factorization. In: Holub, J., Žďárek, J. (eds.) Proceedings of the Prague Stringology Conference 2013, pp. 70–77. Czech Technical University in Prague, Czech Republic (2013)Google Scholar
  3. 3.
    Borozdin, K., Kosolobov, D., Rubinchik, M., Shur, A.M.: Palindromic length in linear time. In: CPM. LIPIcs, vol. 78, pp. 23:1–23:12. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)Google Scholar
  4. 4.
    Fici, G., Gagie, T., Kärkkäinen, J., Kempa, D.: A subquadratic algorithm for minimum palindromic factorization. J. Discret. Algorithms 28, 41–48 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gupta, S., Prasad, R.: Searching gapped palindromes in DNA sequences using Burrows Wheeler type transformation. J. Inf. Optim. Sci. 37(1), 51–74 (2016).  https://doi.org/10.1080/02522667.2015.1103044MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  7. 7.
    Hsu, P., Chen, K., Chao, K.: Finding all approximate gapped palindromes. Int. J. Found. Comput. Sci. 21(6), 925–939 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    I, T., Inenaga, S., Takeda, M.: Palindrome pattern matching. Theor. Comput. Sci. 483, 162–170 (2013).  https://doi.org/10.1016/J.TCS.2012.01.047MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    I, T., Sugimoto, S., Inenaga, S., Bannai, H., Takeda, M.: Computing palindromic factorizations and palindromic covers on-line. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds.) CPM 2014. LNCS, vol. 8486, pp. 150–161. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-07566-2_16CrossRefGoogle Scholar
  10. 10.
    Kolpakov, R., Kucherov, G.: Searching for gapped palindromes. Theor. Comput. Sci. 410(51), 5365–5373 (2009).  https://doi.org/10.1016/j.tcs.2009.09.013MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kosolobov, D., Rubinchik, M., Shur, A.M.: Pa\(^{k}\) is linear recognizable online. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, J.-J., Wattenhofer, R. (eds.) SOFSEM 2015. LNCS, vol. 8939, pp. 289–301. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46078-8_24CrossRefGoogle Scholar
  12. 12.
    Manacher, G.K.: A new linear-time “on-line” algorithm for finding the smallest initial palindrome of a string. J. ACM 22(3), 346–351 (1975)CrossRefGoogle Scholar
  13. 13.
    Narisada, S., Diptarama, Narisawa, K., Inenaga, S., Shinohara, A.: Computing longest single-arm-gapped palindromes in a string. In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds.) SOFSEM 2017. LNCS, vol. 10139, pp. 375–386. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-51963-0_29CrossRefGoogle Scholar
  14. 14.
    Smith, G.R.: Meeting DNA palindromes head-to-head. Genes Dev. 22, 2612–2620 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Keisuke Goto
    • 1
    Email author
  • I Tomohiro
    • 2
  • Hideo Bannai
    • 3
  • Shunsuke Inenaga
    • 3
  1. 1.Fujitsu Laboratories Ltd.KawasakiJapan
  2. 2.Kyushu Institute of TechnologyIizukaJapan
  3. 3.Kyushu UniversityFukuokaJapan

Personalised recommendations