A fast average case algorithm for lyndon decomposition

Abstract

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.

Keywords:

• Combinatorial
• algorithm
• word
• string
• monoid
• Lyndon
• decomposition
• factorization
• canonization
• canonical form
• lexicographically least
• circular
• average case

C.R. Category:

• G.2.1

AMS Subject Classification:

• 68C25

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.

Notes

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.

^*School of Computing, Curtin University of Technology, Perth WA 6001, Australia.