文字列圧縮と組合せ論による大規模データ管理・処理技法の開発

本研究的重点是（a）实用和动态的Trie数据结构，（B）小空间中语法压缩Re-Pair的计算，以及（c）双射Burrows-Wheeler变换（BBWT）的改进，它是Burrows-Wheeler变换（BWT）的一个变体，在理论和实践中都很受欢迎，用于索引字符串数据。(a)我们设计了一种新的紧凑散列方法，这是在实践中最有效的内存方法时，大量的整数键的有界域。基于这种方法，我们提出了动态特里数据结构与路径分解或特里压缩。(b)Re-Pair是一种压缩比很高的语法，在有限的内存中很难计算。在这里，我们可以找到一个计算Re-Pair的二次时间算法，几乎没有额外的空间。我们还设计了一个索引数据结构，建立在一个语法表示林登树。该索引利用了Lyndon词的几个属性，将目前最快的语法索引的运行时间从模式长度的二次因子提高到线性因子。(c)最后，我们可以在BBWT上建立一个索引数据结构，就地计算BBWT或将BWT转换为BBWT，最后在线性时间内建立BBWT。除此之外，我们还可以找到空间有效的分解算法，用于非重叠的LZ 77分解和LZ 78子串压缩问题。这些算法工作在接近线性的时间与空间渐近的输入文本长度位。

The focus of this research was set on (a) practical and dynamic trie data structures, (b) the computation of the grammar compression Re-Pair in small space, and (c) advancements for the bijective Burrows-Wheeler transform (BBWT), a variant of the Burrows-Wheeler transform (BWT) well received in theory as well as in practice for indexing string data.(a) We have devised a novel approach for compact hashing, which is the most memory-efficient approach in practice when working with a huge number of integer keys of a bounded domain. Based on this approach, we have proposed dynamic trie data structures working with path-decomposition or with trie compaction.(b) Re-Pair, a grammar with high compression ratios, is difficult to compute within limited amount of memory. Here, we could find a quadratic time algorithm computing Re-Pair with almost no additional space. We also devised an index data structure build upon a grammar representing the Lyndon tree. This index exploits several properties of the Lyndon words to improve the running time of the currently fastest grammar index from a quadratic factor on the pattern length to a linear one.(c) Finally, we could build an indexing data structure on top of the BBWT, compute the BBWT in-place or transform the BWT into the BBWT, and finally build the BBWT in linear time.Asides from that, we could find space-efficient factorization algorithms for the non-overlapping LZ77 factorization and the LZ78 substring compression problem. These algorithms work in near-linear time with space asymptotic to the input text length in bits.