Palindromic Length in Linear Time

Authors Kirill Borozdin, Dmitry Kosolobov, Mikhail Rubinchik, Arseny M. Shur

Thumbnail PDF


  • Filesize: 0.54 MB
  • 12 pages

Document Identifiers

Author Details

Kirill Borozdin
Dmitry Kosolobov
Mikhail Rubinchik
Arseny M. Shur

Cite AsGet BibTex

Kirill Borozdin, Dmitry Kosolobov, Mikhail Rubinchik, and Arseny M. Shur. Palindromic Length in Linear Time. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 23:1-23:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Palindromic length of a string is the minimum number of palindromes whose concatenation is equal to this string. The problem of finding the palindromic length drew some attention, and a few O(n log n) time online algorithms were recently designed for it. In this paper we present the first linear time online algorithm for this problem.
  • palindrome
  • palindromic length
  • palindromic factorization
  • online


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Vladimir Arlazarov, Efim Dinic, Mikhail Kronrod, and Igor Faradzev. On economical construction of the transitive closure of a directed graph. Dokl. Akad. Nauk SSSR, 194(11):1209-1210, 1970. Google Scholar
  2. Stefan Burkhardt and Juha Kärkkäinen. Fast lightweight suffix array construction and checking. In Ricardo A. Baeza-Yates, Edgar Chávez, and Maxime Crochemore, editors, Proc. of the 14th Annual Symposium on Combinatorial Pattern Matching (CPM 2003), volume 2676 of LNCS, pages 55-69. Springer, 2003. URL:
  3. Gabriele Fici, Travis Gagie, Juha Kärkkäinen, and Dominik Kempa. A subquadratic algorithm for minimum palindromic factorization. J. Discrete Algorithms, 28:41-48, 2014. URL:
  4. Zvi Galil and Joel I. Seiferas. A linear-time on-line recognition algorithm for "palstar". J. ACM, 25(1):102-111, 1978. URL:
  5. Tomohiro I, Shiho Sugimoto, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Computing palindromic factorizations and palindromic covers on-line. In Alexander S. Kulikov, Sergei O. Kuznetsov, and Pavel A. Pevzner, editors, Proceedings of the 25th Annual Symposium on Combinatorial Pattern Matching (CPM 2014), volume 8486 of LNCS, pages 150-161. Springer, 2014. URL:
  6. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. URL:
  7. Dmitry Kosolobov, Mikhail Rubinchik, and Arseny M. Shur. Pal^k is linear recognizable online. In Giuseppe F. Italiano, Tiziana Margaria-Steffen, Jaroslav Pokorný, Jean-Jacques Quisquater, and Roger Wattenhofer, editors, Proceedings of the 41st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2015), volume 8939 of LNCS, pages 289-301. Springer, 2015. URL:
  8. Glenn K. Manacher. A new linear-time "on-line" algorithm for finding the smallest initial palindrome of a string. J. ACM, 22(3):346-351, 1975. URL:
  9. Palindromic Length. Sources and tests for linear palindromic length problem, 2017. URL:
  10. Mikhail Rubinchik and Arseny M. Shur. EERTREE: an efficient data structure for processing palindromes in strings. In Zsuzsanna Lipták and William F. Smyth, editors, Proc. of the 26th International Workshop on Combinatorial Algorithms (IWOCA 2015), volume 9538 of LNCS, pages 321-333. Springer, 2015. URL:
  11. Anatol O. Slisenko. A simplified proof of the real-time recognizability of palindromes on turing machines. J. Soviet. Math., 15(1):68-77, 1977. URL: