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Off-line and on-line algorithms for closed string factorization.
- Source :
-
Theoretical Computer Science . Nov2019, Vol. 792, p12-19. 8p. - Publication Year :
- 2019
-
Abstract
- A string X = X [ 1.. n ] , n > 1 , is said to be closed if it has a nonempty proper prefix that is also a suffix, but that otherwise occurs nowhere else in X ; for n = 1 , every X is closed. Closed strings were introduced by Fici in [1] as objects of combinatorial interest. Recently Badkobeh et al. [2] described a variety of algorithms to factor a given string into closed factors. In particular, they studied the Longest Closed Factorization (LCF) problem, which greedily computes the decomposition X = X 1 X 2 ⋯ X k , where X 1 is the longest closed prefix of X , X 2 the longest closed prefix of X with prefix X 1 removed, and so on. In this paper we present an O (log n) amortized per character algorithm to compute LCF on-line, where n is the length of the string. We also introduce the Minimum Closed Factorization (MCF) problem, which identifies the minimum number of closed factors that cover X. We first describe an off-line O (n log 2 n) -time algorithm to compute M C F (X) , then we present an on-line algorithm for the same problem. In fact, we show that M C F (X) can be computed in O (L log n) time from M C F (X ′) , where X ′ = X [ 1.. n − 1 ] , and L is the largest integer such that the suffix X [ n − L + 1.. n ] is a substring of X ′. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*INTEGERS
*FACTORIZATION
*ONLINE algorithms
Subjects
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 792
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 138832984
- Full Text :
- https://doi.org/10.1016/j.tcs.2018.10.033