关于有无RLE的阿贝尔最长公因子
On Abelian Longest Common Factor with and without RLE
摘要：
我们认为阿贝尔最长公因子问题在两种情况下：当输入字符串是未压缩的，大小为$n$，当输入字符串是游程编码，其压缩表示的大小最多为$m$。字母表大小由$σ$表示。对于未压缩的问题，我们展示了一个$o(n^2)$ -时间和$\Oh(n)$ -空间算法的情况下，$σ=\Oh(1)$，使一个非平凡的使用制表。对于RLE压缩的问题，我们展示了两个算法：一个工作在$\Oh(m^2σ^2 \log^3 m)$时间和$\Oh(m (σ^2+\log^2 m))$空间，它采用线扫描，和一个工作在$\Oh(m^3)$时间和$\Oh(m)$空间，适用于在一个仔细的方式滑动窗口为基础的方法。后者改进了Sugimoto等人最近开发的先前已知的$\Oh(nm^2)$时间和$\Oh(m^4)$时间算法。（IWOCA 2017）和Grabowski（SPIRE 2017）。
英文摘要：
We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$. The alphabet size is denoted by $σ$. For the uncompressed problem, we show an $o(n^2)$-time and $\Oh(n)$-space algorithm in the case of $σ=\Oh(1)$, making a non-trivial use of tabulation. For the RLE-compressed problem, we show two algorithms: one working in $\Oh(m^2σ^2 \log^3 m)$ time and $\Oh(m (σ^2+\log^2 m))$ space, which employs line sweep, and one that works in $\Oh(m^3)$ time and $\Oh(m)$ space that applies in a careful way a sliding-window-based approach. The latter improves upon the previously known $\Oh(nm^2)$-time and $\Oh(m^4)$-time algorithms that were recently developed by Sugimoto et al.\ (IWOCA 2017) and Grabowski (SPIRE 2017), respectively.
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