Dynamic index and LZ factorization in compressed space

Takaaki Nishimoto; Tomohiro I; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda

doi:10.1016/j.dam.2019.01.014

Dynamic index and LZ factorization in compressed space

Takaaki Nishimoto, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Mathematical Informatics

Research output: Contribution to journal › Article

1 Citation (Scopus)

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 [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf_A+zlogwlog³N(log^∗N)²) time with O(w) working space.

Original language	English
Pages (from-to)	116-129
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	274
DOIs	https://doi.org/10.1016/j.dam.2019.01.014
Publication status	Published - Mar 15 2020

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All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

Nishimoto, T., I, T., Inenaga, S., Bannai, H., & Takeda, M. (2020). Dynamic index and LZ factorization in compressed space. Discrete Applied Mathematics, 274, 116-129. https://doi.org/10.1016/j.dam.2019.01.014

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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|fA+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 [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(NfA+zlogwlog3N(log∗N)2) time with O(w) working space.",

author = "Takaaki Nishimoto and Tomohiro I and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda",

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AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2020/3/15

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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|fA+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 [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(NfA+zlogwlog3N(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|fA+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 [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(NfA+zlogwlog3N(log∗N)2) time with O(w) working space.

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10.1016/j.dam.2019.01.014