A new characterization of maximal repetitions by Lyndon trees
SODA(2015)
摘要
We give a new characterization of maximal repetitions (or runs) in strings, using a tree defined on recursive standard factorizations of Lyndon words, called the Lyndon tree. The characterization leads to a remarkably simple novel proof of the linearity of the maximum number of runs ρ(n) in a string of length n. Furthermore, we show an upper bound of ρ(n) < 1.5n, which improves on the best upper bound 1.6n (Crochemore & Ilie 2008) that does not rely on computational verification. The proof also gives rise to a new, conceptually simple linear-time algorithm for computing all the runs in a string. A notable characteristic of our algorithm is that, unlike all existing linear-time algorithms, it does not utilize the Lempel-Ziv factorization of the string.
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