TY - JOUR

T1 - Dynamic index and LZ factorization in compressed space

AU - Nishimoto, Takaaki

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Funding Information:
We would like to thank Paweł Gawrychowski for drawing our attention to the work by Alstrup et al. [2,3] and for fruitful discussions. Tomohiro I was supported by JSPS KAKENHI Grant Number 16K16009 .
Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2020/3/15

Y1 - 2020/3/15

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.

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

AN - SCOPUS:85061439333

VL - 274

SP - 116

EP - 129

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -