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Lyndon Factorization of Grammar Compressed Texts Revisited

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

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

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Abstract

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.

Cite As Get 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) https://doi.org/10.4230/LIPIcs.CPM.2018.24

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

Funding

This work was supported by JSPS KAKENHI Grant Numbers JP17H06923 (YN), JP16K16009 (TI), JP17H01697 (SI), JP16H02783 (HB), and JP25240003 (MT).

References

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