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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Block palindromes were firstly introduced in a problem of 2015 British Informatics Olympiad [1], but we did not know the existence at the first version of this paper.
References
The 2015 British Informatics Olympiad (2015). http://olympiad.org.uk/2015/index.html. Accessed 13 June 2018
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)
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)
Fici, G., Gagie, T., Kärkkäinen, J., Kempa, D.: A subquadratic algorithm for minimum palindromic factorization. J. Discret. Algorithms 28, 41–48 (2014)
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/10.1080/02522667.2015.1103044
Gusfield, D.: Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)
Hsu, P., Chen, K., Chao, K.: Finding all approximate gapped palindromes. Int. J. Found. Comput. Sci. 21(6), 925–939 (2010)
I, T., Inenaga, S., Takeda, M.: Palindrome pattern matching. Theor. Comput. Sci. 483, 162–170 (2013). https://doi.org/10.1016/J.TCS.2012.01.047
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_16
Kolpakov, R., Kucherov, G.: Searching for gapped palindromes. Theor. Comput. Sci. 410(51), 5365–5373 (2009). https://doi.org/10.1016/j.tcs.2009.09.013
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_24
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)
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_29
Smith, G.R.: Meeting DNA palindromes head-to-head. Genes Dev. 22, 2612–2620 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Goto, K., Tomohiro, I., Bannai, H., Inenaga, S. (2018). Block Palindromes: A New Generalization of Palindromes. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-00479-8_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00478-1
Online ISBN: 978-3-030-00479-8
eBook Packages: Computer ScienceComputer Science (R0)