| Budget Amount *help |
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2020: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2019: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2018: ¥400,000 (Direct Cost: ¥400,000)
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| Outline of Annual Research Achievements |
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.
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