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 | |
| 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.
In: Discrete Applied Mathematics, 01.01.2019.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.
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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 -