Mathematics in Computer Science

, Volume 11, Issue 2, pp 219–232 | Cite as

Palindromic Subsequence Automata and Longest Common Palindromic Subsequence

  • Md. Mahbubul Hasan
  • A. S. M. Sohidull Islam
  • M. Sohel Rahman
  • Ayon Sen


In this paper, we present a novel weighted finite automaton called palindromic subsequence automaton (PSA) that is a compact representation of all the palindromic subsequences of a string. Then we use PSA to solve the longest common palindromic subsequence problem. Our automata based algorithms are efficient both in theory and in practice.


Finite automata Palindromes Palindromic subsequences Algorithms 

Mathematics Subject Classification

68Q45 68W32 


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  1. 1.
    Breslauer, D., Galil, Z.: Finding all periods and initial palindromes of a string in parallel. Algorithmica 14(4), 355–366 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Chen, K.-Y., Hsu, P.-H., Chao, K.-M.: Identifying approximate palindromes in run-length encoded strings. ISAAC 2, 339–350 (2010)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Choi, C.Q.: DNA palindromes found in cancer. The Scientist (2005)Google Scholar
  4. 4.
    Chowdhury, S.R., Hasan, M.M., Iqbal, S., Rahman, M.S.: Computing a longest common palindromic subsequence. Fundam. Inform. 129(4), 329–340 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chuang, K., Lee, R., Huang, C.: Finding all palindrome subsequences in a string. In: The 24th Workshop on Combinatorial Mathematics and Computation Theory (2007)Google Scholar
  6. 6.
    Farhana, E., Rahman, M.S.: Doubly-constrained LCS and hybrid-constrained LCS problems revisited. Inf. Process. Lett. 112(13), 562–565 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Galil, Z.: Real-time algorithms for string-matching and palindrome recognition. In: STOC, pp. 161–173 (1976)Google Scholar
  8. 8.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences—Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  9. 9.
    Hoshino, H., Shinohara, A., Takeda, M., Arikawa, S.: Online construction of subsequence automata for multiple texts. In: SPIRE, pp. 146–152 (2000)Google Scholar
  10. 10.
    Hsu, P.-H., Chen, K.-Y., Chao, K.-M.: Finding all approximate gapped palindromes. In: ISAAC, pp. 1084–1093 (2009)Google Scholar
  11. 11.
  12. 12.
  13. 13.
    Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest subsequences. Commun. ACM 20(5), 350–353 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Tomohiro, I., Inenaga, S., Takeda, M.: Palindrome pattern matching. In: CPM, pp. 232–245 (2011)Google Scholar
  15. 15.
    Iliopoulos, C.S., Rahman, M.S.: Algorithms for computing variants of the longest common subsequence problem. Theor. Comput. Sci. 395(2–3), 255–267 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Iliopoulos, C.S., Rahman, M.S.: New efficient algorithms for the LCS and constrained LCS problems. Inf. Process. Lett. 106(1), 13–18 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Iliopoulos, C.S., Rahman, M.S.: A new efficient algorithm for computing the longest common subsequence. Theory Comput. Syst. 45(2), 355–371 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Iliopoulos, C.S., Rahman, M.S., Vorácek, M., Vagner, L.: Finite automata based algorithms on subsequences and supersequences of degenerate strings. J. Discrete Algorithms 8(2), 117–130 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kolpakov, R., Kucherov, G.: Searching for gapped palindromes. Theor. Comput. Sci. 410(51), 5365–5373 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    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)CrossRefzbMATHGoogle Scholar
  21. 21.
    Matsubara, W., Inenaga, S., Ishino, A., Shinohara, A., Nakamura, T., Hashimoto, K.: Efficient algorithms to compute compressed longest common substrings and compressed palindromes. Theor. Comput. Sci. 410(8–10), 900–913 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Melichar, B., Holub, J., Muzatko, P.: Language and Translation. Publishing House of CTU (1997)Google Scholar
  23. 23.
    Porto, A.H.L., Barbosa, V.C.: Finding approximate palindromes in strings. Pattern Recognit. 35(11), 2581–2591 (2002)CrossRefzbMATHGoogle Scholar
  24. 24.
    Tanaka, H., Bergstrom, D.A., Yao, M.-C., Tapscott, S.J.: Widespread and nonrandom distribution of dna palindromes in cancer cells provides a structural platform for subsequent gene amplification. Nat. Genet. 37(3), 320–327 (2005)CrossRefGoogle Scholar
  25. 25.
    Tanaka, H., Tapscott, S.J., Trask, B.J., Yao, M.C.: Short inverted repeats initiate gene amplification through the formation of a large DNA palindrome in mammalian cells. Natl. Acad. Sci. 99(13), 8772–8777 (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Md. Mahbubul Hasan
    • 1
    • 2
  • A. S. M. Sohidull Islam
    • 1
    • 3
  • M. Sohel Rahman
    • 1
  • Ayon Sen
    • 1
    • 4
  1. 1.AℓEDA Group, Department of CSEBUETDhakaBangladesh
  2. 2.GoogleZurichGermany
  3. 3.School of Computational Science and EngineeringMcMaster UniversityHamiltonCanada
  4. 4.Department of Computer SciencesUniversity of Wisconsin-MadisonMadisonUSA

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