Dynamic index and LZ factorization in compressed space

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

doi:10.1016/j.dam.2019.01.014

Dynamic index and LZ factorization in compressed space

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

Mathematical Informatics

Research output: Contribution to journal › Article

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
Journal	Discrete Applied Mathematics
DOIs	https://doi.org/10.1016/j.dam.2019.01.014
Publication status	Published - Jan 1 2019

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Factorization

Deletion

Insertion

Encoding

Signature

Text

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

Nishimoto, T., Tomohiro, I., Inenaga, S., Bannai, H., & Takeda, M. (2019). Dynamic index and LZ factorization in compressed space. Discrete Applied Mathematics. https://doi.org/10.1016/j.dam.2019.01.014

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

In: Discrete Applied Mathematics, 01.01.2019.

Research output: Contribution to journal › Article

Nishimoto, T, Tomohiro, I, Inenaga, S , Bannai, H & Takeda, M 2019, 'Dynamic index and LZ factorization in compressed space', Discrete Applied Mathematics. https://doi.org/10.1016/j.dam.2019.01.014

Nishimoto T, Tomohiro I, Inenaga S , Bannai H , Takeda M. Dynamic index and LZ factorization in compressed space. Discrete Applied Mathematics. 2019 Jan 1. https://doi.org/10.1016/j.dam.2019.01.014

Nishimoto, Takaaki ; Tomohiro, I. ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki. / Dynamic index and LZ factorization in compressed space. In: Discrete Applied Mathematics. 2019.

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10.1016/j.dam.2019.01.014