R-enum：BWT游程有界空间中特征子串的计数
R-enum: Enumeration of Characteristic Substrings in BWT-runs Bounded Space
摘要：
枚举特征子串（例如，最大重复、最小唯一子串和最小缺失字）已经成为重要的研究课题，因为在诸如串处理和计算生物学的各种领域中存在各种各样的应用。虽然已经提出了几种特征子串的枚举算法，但它们的空间使用率与输入串的长度成正比，因此它们不是空间有效的。最近，游程编码Burrows-Wheeler变换（RLBWT）在字符串处理中引起了越来越多的关注，并且已经开发了各种RLBWT算法。然而，使用RLBWT开发特征子串的枚举算法仍然是一个挑战。本文提出了第一个基于RLBWT的特征子串枚举算法r-enum（RLBWT-based enumeration）。R-enum在$O(n \log \log (n/r))$时间内运行，并且对于字符串长度$n$和RLBWT中的运行次数$r$，具有$O(r \log n)$位的工作空间，其中对于高度重复的字符串，预期$r$显著小于$n$（即，重复多次的字符串）。使用高度重复字符串的基准数据集的实验表明，r-enum的结果比以前的结果更节省空间。此外，我们证明了r-enum的适用性，以一个巨大的字符串进行实验的300千兆字节的字符串的100个人类基因组。
英文摘要：
Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such as string processing and computational biology. Although several enumeration algorithms for characteristic substrings have been proposed, they are not space-efficient in that their space-usage is proportional to the length of an input string. Recently, the run-length encoded Burrows-Wheeler transform (RLBWT) has attracted increased attention in string processing, and various algorithms for the RLBWT have been developed. Developing enumeration algorithms for characteristic substrings with the RLBWT, however, remains a challenge. In this paper, we present r-enum (RLBWT-based enumeration), the first enumeration algorithm for characteristic substrings based on RLBWT. R-enum runs in $O(n \log \log (n/r))$ time and with $O(r \log n)$ bits of working space for string length $n$ and number $r$ of runs in RLBWT, where $r$ is expected to be significantly smaller than $n$ for highly repetitive strings (i.e., strings with many repetitions). Experiments using a benchmark dataset of highly repetitive strings show that the results of r-enum are more space-efficient than the previous results. In addition, we demonstrate the applicability of r-enum to a huge string by performing experiments on a 300-gigabyte string of 100 human genomes.
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