关于最长公阿贝尔因子问题的注记
A note on the longest common Abelian factor problem
摘要：
阿贝尔字符串匹配问题在过去几年中成为一个相当感兴趣的对象。最近，Alatabbi等人的\cite{AILR2015}给出了一对字符串的最长公共阿贝尔因子问题的第一个解决方案，用$O(σn \log n)$空间位达到$O(σn^2)$时间，其中$n$是字符串的长度，$σ$是字母表的大小。在本文中，我们将展示如何在保持时间复杂度的同时，将空间减少$σ$的一个因子，然后在允许超线性空间的情况下，如果字母表不太小，则如何提高时间复杂度。
英文摘要：
Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings, reaching $O(σn^2)$ time with $O(σn \log n)$ bits of space, where $n$ is the length of the strings and $σ$ is the alphabet size. In this note we show how the time complexity can be preserved while the space is reduced by a factor of $σ$, and then how the time complexity can be improved, if the alphabet is not too small, when superlinear space is allowed.
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。
