压缩Tries中的路径定位
On Locating Paths in Compressed Tries
摘要：
在本文中，我们考虑的问题，压缩一个trie树，同时支持强大的\emph{locate}查询：返回的前序标识符的所有节点达到一个给定的查询模式标记的路径。我们的结果建立在Ferragina等人[FOCS 2005]的XBWT树变换之上，并基于游程编码的Burrows-Wheeler变换（BWT）推广了Gagie等人[SODA 2018，JACM 2020]的\emph{r-index}定位机制。我们的第一个贡献是提出一个合适的推广的游程BWT尝试。我们表明，这种自然的推广享有几个有用的属性，其对应的字符串：特别是，转换原生支持计数出现的查询模式的特里的路径和它的大小$r$捕获特里的重复性和下界特里熵的自然概念。我们的主要贡献是更深入地了解这个对象的组合结构。详细地说，我们表明，一个数据结构的$O(r\log n) + 2n + o(n)$位，其中$n$是节点的数量，允许定位的$occ$出现的模式的长度$m$在接近最佳的$O(m\logσ+ occ)$时间，其中$σ$是字母表的大小。我们的解决方案包括在采样$O(r)$节点，可用作“锚点”在定位过程中。一旦获得的前序标识符的第一个模式出现（共字典顺序），我们表明，这些锚点之间的恒定时间跳跃的一个常数导致下一个模式出现的标识符，从而使定位在最佳的$O(1)$每次出现的时间。
英文摘要：
In this paper, we consider the problem of compressing a trie while supporting the powerful \emph{locate} queries: to return the pre-order identifiers of all nodes reached by a path labeled with a given query pattern. Our result builds on top of the XBWT tree transform of Ferragina et al. [FOCS 2005] and generalizes the \emph{r-index} locate machinery of Gagie et al. [SODA 2018, JACM 2020] based on the run-length encoded Burrows-Wheeler transform (BWT). Our first contribution is to propose a suitable generalization of the run-length BWT to tries. We show that this natural generalization enjoys several of the useful properties of its counterpart on strings: in particular, the transform natively supports counting occurrences of a query pattern on the trie's paths and its size $r$ captures the trie's repetitiveness and lower-bounds a natural notion of trie entropy. Our main contribution is a much deeper insight into the combinatorial structure of this object. In detail, we show that a data structure of $O(r\log n) + 2n + o(n)$ bits, where $n$ is the number of nodes, allows locating the $occ$ occurrences of a pattern of length $m$ in nearly-optimal $O(m\logσ+ occ)$ time, where $σ$ is the alphabet's size. Our solution consists in sampling $O(r)$ nodes that can be used as "anchor points" during the locate process. Once obtained the pre-order identifier of the first pattern occurrence (in co-lexicographic order), we show that a constant number of constant-time jumps between those anchor points lead to the identifier of the next pattern occurrence, thus enabling locating in optimal $O(1)$ time per occurrence.
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。
