AI 中文总结
该研究提出最优空间的常数时间逆后缀数组结构，在字RAM中确定性构造该结构及两类后缀数组，匹配二元文本的时间-空间下界，可提升字典匹配算法效率。
AI 中文摘要
对于文本 $T\in[0..\sigma)^n$（其中 $2\leq\sigma\leq n$），其后缀数组按字典序排列后缀起始位置，而逆后缀数组将每个位置映射到对应后缀的秩。自2000年压缩后缀数组与FM-index出现以来，核心目标是在 $O(n\log\sigma)$ 比特空间内支持这两种查询。Thankachan近期将逆后缀数组查询时间降至 $O(\log\log n/\log\log\sigma)$，但常数时间的实现仍未解决。我们提出首个兼具最优空间与查询时间的逆后缀数组结构：空间为 $O(n\log\sigma)$ 比特，查询时间为 $O(1)$。对于二元文本，该结构无条件分离了确定性结构下的两种查询，因为在单元探测模型中，每个 $O(n)$ 比特的后缀数组结构（单元大小为 $\Theta(\log n)$ 比特）的最坏情况查询时间为 $\Omega(\log\log n/\log\log\log n)$。构造是另一项挑战：线性时间构造可能需要 $\Theta(\log_{\sigma} n)$ 倍于读取输入或写入紧凑索引的时间。此前仅有一种支持两种查询的索引已知存在亚线性构造。在字长为 $\Theta(\log n)$ 比特的字RAM中，我们从打包文本确定性构造了该新结构及两类后缀数组，时间为 $O(n\min(1,\log\sigma/\sqrt{\log n}))$。对于 $B\geq2$，第一类使用 $O(n\log\sigma(1+\log_B\log_{\sigma} n))$ 比特空间，查询时间为 $O(B(1+\log_B\log_{\sigma} n))$；第二类使用 $O(Bn\log\sigma(1+\log_B\log_{\sigma} n))$ 比特空间，查询时间为 $O(1+\log_B\log_{\sigma} n)$。每类的峰值预处理空间均受限于其索引大小。对于二元文本，当 $B\geq(\log\log n)^{\Omega(1)}$ 时，第二类匹配确定性单元探测时间-空间下界；在最慢查询场景之外，若将确定性构造时间改进为 $o(n/\sqrt{\log n})$，将得到同样快速的字典匹配算法。
英文摘要
For a text $T\in[0..σ)^n$ with $2\leqσ\leq n$, its suffix array orders the suffix starting positions lexicographically, while its inverse suffix array maps each position to its suffix's rank. Since compressed suffix arrays and FM-indexes appeared in 2000, a central goal has been to support both queries in $O(n\logσ)$ bits. Thankachan recently reduced inverse suffix array query time to $O(\log\log n/\log\logσ)$, but constant time remained open. We give the first inverse suffix array structure with optimal space and query time: $O(n\logσ)$ bits and $O(1)$ time. For binary texts, this unconditionally separates the two queries for deterministic structures, since every $O(n)$-bit suffix array structure in the cell-probe model with $Θ(\log n)$-bit cells has worst-case query time $Ω(\log\log n/\log\log\log n)$. Construction is a second challenge: linear time can take $Θ(\log_σ n)$ times as long as reading the input or writing a compact index. Previously, sublinear construction was known for only one such index supporting both queries. In the word RAM with $Θ(\log n)$-bit words, we deterministically construct the new structure and two suffix array families from the packed text in $O(n\min(1,\logσ/\sqrt{\log n}))$ time. For $B\geq2$, the first family uses $O(n\logσ(1+\log_B\log_σn))$ bits and has query time $O(B(1+\log_B\log_σn))$, whereas the second uses $O(Bn\logσ(1+\log_B\log_σn))$ bits and has query time $O(1+\log_B\log_σn)$. Each has peak preprocessing space bounded by its index size. For binary texts, the second family matches the deterministic cell-probe time-space lower bound whenever $B\geq(\log\log n)^{Ω(1)}$, and, outside the slowest-query regimes, improving the deterministic construction time to $o(n/\sqrt{\log n})$ would yield an equally fast Dictionary Matching algorithm.
