### Abstract

In this paper, we propose a new dynamic compressed index of O(w) space for a dynamic text T, where w=O(min(zlogNlog ^{∗} M,N)) is the size of the signature encoding of T, z is the size of the Lempel–Ziv77 (LZ77) factorization of T, N is the length of T, and M≥N is the maximum length of T. Our index supports searching for a pattern P in T in O(|P|f _{A} +logwlog|P|log ^{∗} M(logN+log|P|log ^{∗} M)+occlogN) time and insertion/deletion of a substring of length y in O((y+logNlog ^{∗} M)logwlogNlog ^{∗} M) time, where occ is the number of occurrences of P in T and f _{A} =O(min{[Formula presented],[Formula presented]}). Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf _{A} +zlogwlog ^{3} N(log ^{∗} N) ^{2} ) time with O(w) working space.

Original language | English |
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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

**Dynamic index and LZ factorization in compressed space.** / Nishimoto, Takaaki; Tomohiro, I.; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Dynamic index and LZ factorization in compressed space

AU - Nishimoto, Takaaki

AU - Tomohiro, I.

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we propose a new dynamic compressed index of O(w) space for a dynamic text T, where w=O(min(zlogNlog ∗ M,N)) is the size of the signature encoding of T, z is the size of the Lempel–Ziv77 (LZ77) factorization of T, N is the length of T, and M≥N is the maximum length of T. Our index supports searching for a pattern P in T in O(|P|f A +logwlog|P|log ∗ M(logN+log|P|log ∗ M)+occlogN) time and insertion/deletion of a substring of length y in O((y+logNlog ∗ M)logwlogNlog ∗ M) time, where occ is the number of occurrences of P in T and f A =O(min{[Formula presented],[Formula presented]}). Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf A +zlogwlog 3 N(log ∗ N) 2 ) time with O(w) working space.

AB - In this paper, we propose a new dynamic compressed index of O(w) space for a dynamic text T, where w=O(min(zlogNlog ∗ M,N)) is the size of the signature encoding of T, z is the size of the Lempel–Ziv77 (LZ77) factorization of T, N is the length of T, and M≥N is the maximum length of T. Our index supports searching for a pattern P in T in O(|P|f A +logwlog|P|log ∗ M(logN+log|P|log ∗ M)+occlogN) time and insertion/deletion of a substring of length y in O((y+logNlog ∗ M)logwlogNlog ∗ M) time, where occ is the number of occurrences of P in T and f A =O(min{[Formula presented],[Formula presented]}). Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf A +zlogwlog 3 N(log ∗ N) 2 ) time with O(w) working space.

UR - http://www.scopus.com/inward/record.url?scp=85061439333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061439333&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2019.01.014

DO - 10.1016/j.dam.2019.01.014

M3 - Article

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -