# Closed factorization

Golnaz Badkobeh, Hideo Bannai, Keisuke Goto, Tomohiro I, Costas S. Iliopoulos, Shunsuke Inenaga, Simon J. Puglisi, Shiho Sugimoto

5 引用 (Scopus)

### 抄録

A closed string is a string with a proper substring that occurs in the string as a prefix and a suffix, but not elsewhere. Closed strings were introduced by Fici (2011) as objects of combinatorial interest in the study of Trapezoidal and Sturmian words. In this paper we present algorithms for computing closed factors (substrings) in strings. First, we consider the problem of greedily factorizing a string into a sequence of longest closed factors. We describe an algorithm for this problem that uses linear time and space. We then consider the related problem of computing, for every position in the string, the longest closed factor starting at that position. We describe a simple algorithm for the problem that runs in O(nlogn/loglogn) time, where n is the length of the string. This also leads to an algorithm to compute the maximal closed factor containing (i.e. covering) each position in the string in O(nlogn/loglogn) time. We also present linear time algorithms to factorize a string into a sequence of shortest closed factors of length at least two, to compute the shortest closed factor of length at least two starting at each position of the string, and to compute a minimal closed factor of length at least two containing each position of the string.

元の言語 英語 23-29 7 Discrete Applied Mathematics 212 https://doi.org/10.1016/j.dam.2016.04.009 出版済み - 10 30 2016

### Fingerprint

Factorization
Strings
Closed
Sturmian Words
Factorise
Suffix
Computing
Prefix
Linear-time Algorithm
Linear Space
Linear Time
Covering

### All Science Journal Classification (ASJC) codes

• Discrete Mathematics and Combinatorics
• Applied Mathematics

### これを引用

Badkobeh, G., Bannai, H., Goto, K., I, T., Iliopoulos, C. S., Inenaga, S., ... Sugimoto, S. (2016). Closed factorization. Discrete Applied Mathematics, 212, 23-29. https://doi.org/10.1016/j.dam.2016.04.009

Closed factorization. / Badkobeh, Golnaz; Bannai, Hideo; Goto, Keisuke; I, Tomohiro; Iliopoulos, Costas S.; Inenaga, Shunsuke; Puglisi, Simon J.; Sugimoto, Shiho.

：: Discrete Applied Mathematics, 巻 212, 30.10.2016, p. 23-29.

Badkobeh, G, Bannai, H, Goto, K, I, T, Iliopoulos, CS, Inenaga, S, Puglisi, SJ & Sugimoto, S 2016, 'Closed factorization', Discrete Applied Mathematics, 巻. 212, pp. 23-29. https://doi.org/10.1016/j.dam.2016.04.009
Badkobeh G, Bannai H, Goto K, I T, Iliopoulos CS, Inenaga S その他. Closed factorization. Discrete Applied Mathematics. 2016 10 30;212:23-29. https://doi.org/10.1016/j.dam.2016.04.009
Badkobeh, Golnaz ; Bannai, Hideo ; Goto, Keisuke ; I, Tomohiro ; Iliopoulos, Costas S. ; Inenaga, Shunsuke ; Puglisi, Simon J. ; Sugimoto, Shiho. / Closed factorization. ：: Discrete Applied Mathematics. 2016 ; 巻 212. pp. 23-29.
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AU - Puglisi, Simon J.

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