在线性时间内找出单词中最大的重复次数

R. Kolpakov, G. Kucherov
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引用次数: 334

摘要

单词w中的重复是一个子词,其周期最多为子词长度的一半。我们研究w中出现的最大重复,即w的任何扩展子词具有更大周期的重复。我们首先证明了一个组合结果,即长度为n的单词的所有最大重复的指数之和由n中的一个线性函数限定。这特别表明,在一个单词中只有一个线性数目的最大重复。这允许我们构造一个线性时间算法来找到所有的最大重复。讨论了这些结果的一些后果和应用,以及相关的工作。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Finding maximal repetitions in a word in linear time
A repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first prove a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length n is bounded by a linear function in n. This implies, in particular that there is only a linear number of maximal repetitions in a word. This allows us to construct a linear-time algorithm for finding all maximal repetitions. Some consequences and applications of these results are discussed, as well as related works.
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