A fast average case algorithm for lyndon decomposition

A simple algorithm, called LD, is described for computing the Lyndon decomposition of a word of length. Although LD requires time 0(n log n) in the worst case, it is shown to require only ®(rc) worst-case time for words which are "1-decomposable", and ⊝(n) average-case time for words whose...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 57; no. 1-2; pp. 15 - 31
Main Authors: Iliopoulos, C. S., Smyth, W. F.
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers S.A 01.01.1995
Taylor and Francis
Subjects:
algorithm
Algorithmics. Computability. Computer arithmetics
Applied sciences
average case
canonical form
canonization
circular
Classical combinatorial problems
Combinatorial
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
decomposition
Exact sciences and technology
factorization
G.2.1
lexicographically least
Lyndon
Mathematics
monoid
Sciences and techniques of general use
string
Theoretical computing
word
Average case performance
Finite word
Monoid
Algorithm
Time complexity
Factorization
Canonical form
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:A simple algorithm, called LD, is described for computing the Lyndon decomposition of a word of length. Although LD requires time 0(n log n) in the worst case, it is shown to require only ®(rc) worst-case time for words which are "1-decomposable", and ⊝(n) average-case time for words whose length is small with respect to alphabet size. The main interest in LD resides in its application to the problem of computing the canonical form of a circular word. For this problem, LD is shown to execute significantly faster than other known algorithms on important classes of words. Further, experiment suggests that, when applied to arbitrary words, LD on average outperforms the other known canonization algorithms in terms of two measures: number of tests on letters and execution time.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169508804408