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arXiv 1605.09558cs.DS
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压缩空间中的动态指标与LZ分解

Dynamic index and LZ factorization in compressed space

Takaaki Nishimoto, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

备注：
arXiv admin note: substantial text overlap with arXiv:1605.01488; text overlap with arXiv:1504.06954
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摘要：

本文针对动态文本$T$，提出了一种新的$O(w)$空间的\emph{dynamic compressed index}，其中$w = O(\min(z \log N \log^*M, N))$是$T$的签名编码的大小，$z$是$T$的Lempel-Ziv 77（LZ 77）分解的大小，$N$是$T$的长度，$M \geq 3N$是字RAM模型下可以在常数时间内处理的整数.我们的索引支持在$O(|P| f_{\mathcal{A}} + \log w \log |P| \log^* M (\log N + \log |P| \log^* M) + \mathit{occ} \log N)$时间内在$T$中搜索模式$P$，并在$O((y+ \log N\log^* M)\log w \log N \log^* M)$时间内插入/删除长度为$y$的子串，其中$f_{\mathcal{A}} = O(\min \{ \frac{\log\log M \log\log w}{\log\log\log M}, \sqrt{\frac{\log w}{\log\log w}} \})$。此外，我们提出了一个新的空间有效的LZ 77分解算法的长度$N$，它运行在$O(N f_{\mathcal{A}} + z \log w \log^3 N (\log^* N)^2)$时间与$O(w)$工作空间的给定文本。

英文摘要：

In this paper, we propose a new \emph{dynamic compressed index} of $O(w)$ space for a dynamic text $T$, where $w = O(\min(z \log N \log^*M, N))$ is the size of the signature encoding of $T$, $z$ is the size of the Lempel-Ziv77 (LZ77) factorization of $T$, $N$ is the length of $T$, and $M \geq 3N$ is an integer that can be handled in constant time under word RAM model. Our index supports searching for a pattern $P$ in $T$ in $O(|P| f_{\mathcal{A}} + \log w \log |P| \log^* M (\log N + \log |P| \log^* M) + \mathit{occ} \log N)$ time and insertion/deletion of a substring of length $y$ in $O((y+ \log N\log^* M)\log w \log N \log^* M)$ time, where $f_{\mathcal{A}} = O(\min \{ \frac{\log\log M \log\log w}{\log\log\log M}, \sqrt{\frac{\log w}{\log\log w}} \})$. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text of length $N$, which runs in $O(N f_{\mathcal{A}} + z \log w \log^3 N (\log^* N)^2)$ time with $O(w)$ working space.

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。

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