Lyndon Factorization of Grammar Compressed Texts Revisited

Authors Isamu Furuya, Yuto Nakashima, Tomohiro I , Shunsuke Inenaga, Hideo Bannai , Masayuki Takeda

Thumbnail PDF


  • Filesize: 0.49 MB
  • 10 pages

Document Identifiers

Author Details

Isamu Furuya
  • Graduate School of IST, Hokkaido University, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Japan
Tomohiro I
  • Frontier Research Academy for Young Researchers, Kyushu Institute of Technology, Japan
Shunsuke Inenaga
  • Department of Informatics, Kyushu University, Japan
Hideo Bannai
  • Department of Informatics, Kyushu University, Japan, RIKEN Center for Advanced Intelligence Project, Japan
Masayuki Takeda
  • Department of Informatics, Kyushu University, Japan

Cite AsGet BibTex

Isamu Furuya, Yuto Nakashima, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Lyndon Factorization of Grammar Compressed Texts Revisited. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 24:1-24:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We revisit the problem of computing the Lyndon factorization of a string w of length N which is given as a straight line program (SLP) of size n. For this problem, we show a new algorithm which runs in O(P(n, N) + Q(n, N)n log log N) time and O(n log N + S(n, N)) space where P(n, N), S(n,N), Q(n,N) are respectively the pre-processing time, space, and query time of a data structure for longest common extensions (LCE) on SLPs. Our algorithm improves the algorithm proposed by I et al. (TCS '17), and can be more efficient than the O(N)-time solution by Duval (J. Algorithms '83) when w is highly compressible.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Lyndon word
  • Lyndon factorization
  • Straight line program


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


  1. Alberto Apostolico and Maxime Crochemore. Fast parallel Lyndon factorization with applications. Mathematical Systems Theory, 28(2):89-108, 1995. Google Scholar
  2. Srecko Brlek, Jacques-Olivier Lachaud, Xavier Provençal, and Christophe Reutenauer. Lyndon + Christoffel = digitally convex. Pattern Recognition, 42(10):2239-2246, 2009. Google Scholar
  3. Moses Charikar, Eric Lehman, Ding Liu, Rina Panigrahy, Manoj Prabhakaran, Amit Sahai, and abhi shelat. The smallest grammar problem. IEEE Transactions on Information Theory, 51(7):2554-2576, 2005. Google Scholar
  4. K. T. Chen, R. H. Fox, and R. C. Lyndon. Free differential calculus. iv. the quotient groups of the lower central series. Annals of Mathematics, 68(1):81-95, 1958. Google Scholar
  5. Jacqueline W. Daykin, Costas S. Iliopoulos, and William F. Smyth. Parallel RAM algorithms for factorizing words. Theor. Comput. Sci., 127(1):53-67, 1994. Google Scholar
  6. Jean-Pierre Duval. Factorizing words over an ordered alphabet. J. Algorithms, 4(4):363-381, 1983. Google Scholar
  7. Joseph Yossi Gil and David Allen Scott. A bijective string sorting transform. CoRR, abs/1201.3077, 2012. Google Scholar
  8. Tomohiro I. Longest common extensions with recompression. In Proc. CPM 2017, pages 18:1-18:15, 2017. Google Scholar
  9. Tomohiro I, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Efficient Lyndon factorization of grammar compressed text. In Proc. CPM 2013, pages 153-164, 2013. Google Scholar
  10. Tomohiro I, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster Lyndon factorization algorithms for SLP and LZ78 compressed text. Theor. Comput. Sci., 656:215-224, 2016. Google Scholar
  11. Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, and Arseny M. Shur. On the size of Lempel-Ziv and Lyndon factorizations. In Proc. STACS 2017, pages 45:1-45:13, 2017. Google Scholar
  12. Tomasz Kociumaka. Minimal suffix and rotation of a substring in optimal time. In Proc. CPM 2016, pages 28:1-28:12, 2016. Google Scholar
  13. Manfred Kufleitner. On bijective variants of the Burrows-Wheeler transform. In Proc. PSC 2009, pages 65-79, 2009. Google Scholar
  14. Wojciech Rytter. Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci., 302(1-3):211-222, 2003. URL: