词部分覆盖的快速算法
Fast Algorithm for Partial Covers in Words
摘要：
如果$w$中的每个位置都位于$w$中的某个出现的$u$内，则单词$w$的因子$u$是$w$的覆盖。因此，由$u$覆盖的词$w$概括了重复的概念，即，由$u$的精确连接组成的词。本文引入了$α$的一个新概念--部分覆盖，它可以看作是覆盖的一个松弛变体，即一个因子至少覆盖了$w$中的$α$位置.我们开发了一个数据结构的$O(n)$大小（其中$n=|w|$），可以在$O(n\log n)$的时间，我们适用于计算所有最短的$α$部分覆盖给定的$α$。我们还采用它的$O(n\log n)$时间算法计算最短的$α$ -部分覆盖每个$α=1,2,\ldots,n$。
英文摘要：
A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$. In this article we introduce a new notion of $α$-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least $α$ positions in $w$. We develop a data structure of $O(n)$ size (where $n=|w|$) that can be constructed in $O(n\log n)$ time which we apply to compute all shortest $α$-partial covers for a given $α$. We also employ it for an $O(n\log n)$-time algorithm computing a shortest $α$-partial cover for each $α=1,2,\ldots,n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
