### Abstract

We present two efficient algorithms which, given a compressed representation of a string w of length N, compute the Lyndon factorization of w. Given a straight line program (SLP) S of size n that describes w, the first algorithm runs in O(n^{2}+P(n,N)+Q(n,N)nlogn) time and O(n^{2}+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. Given the Lempel–Ziv 78 encoding of size s for w, the second algorithm runs in O(slogs) time and space.

Original language | English |
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Pages (from-to) | 215-224 |

Number of pages | 10 |

Journal | Theoretical Computer Science |

Volume | 656 |

DOIs | |

Publication status | Published - Dec 20 2016 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**Faster Lyndon factorization algorithms for SLP and LZ78 compressed text.** / I, Tomohiro; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Faster Lyndon factorization algorithms for SLP and LZ78 compressed text

AU - I, Tomohiro

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2016/12/20

Y1 - 2016/12/20

N2 - We present two efficient algorithms which, given a compressed representation of a string w of length N, compute the Lyndon factorization of w. Given a straight line program (SLP) S of size n that describes w, the first algorithm runs in O(n2+P(n,N)+Q(n,N)nlogn) time and O(n2+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. Given the Lempel–Ziv 78 encoding of size s for w, the second algorithm runs in O(slogs) time and space.

AB - We present two efficient algorithms which, given a compressed representation of a string w of length N, compute the Lyndon factorization of w. Given a straight line program (SLP) S of size n that describes w, the first algorithm runs in O(n2+P(n,N)+Q(n,N)nlogn) time and O(n2+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. Given the Lempel–Ziv 78 encoding of size s for w, the second algorithm runs in O(slogs) time and space.

UR - http://www.scopus.com/inward/record.url?scp=84961175476&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961175476&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2016.03.005

DO - 10.1016/j.tcs.2016.03.005

M3 - Article

AN - SCOPUS:84961175476

VL - 656

SP - 215

EP - 224

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -