| 研究実績の概要 |
During fiscal year 2023, we worked on variations of the Burrows-Wheeler transform, one built on a grammar, the positional one, and the Wheeler graph.
Firstly, by storing additionally to the FM-index the index of our DCC'22 paper, we made use of both to accelerate counting queries for all pattern lengths at the expense of more space compared to the FM-index. While the FM-index matches a pattern character-wise, we can switch to the DCC'22-version matching blocks of characters of the pattern defined by the grammar.
Second, we proposed space-efficient data structures that augment the positional Burrows-Wheeler transform for efficiently finding set-maximal exact matches, and compare these with the baseline approach, which uses the plain divergence array.
Thirdly, we worked on matching statistics on Wheeler DFAs, which allows us to match a pattern with multiple reference genome represented by a de-Brujin graph efficiently. Known results use a plain longest common prefix array, which takes space linear to the number of states. We proposed a space-efficient representation that requires a linear number in bits with logarithmic access time. We also give matching statistics computation as an application, which we now can do with a time-space trade-off.
As a side-result, we worked on the substring compression problem for derivates of the LZ78 factorization, which seem to be practically relevant. Here, we used the suffix tree as an index to quickly compute an LZ78-kind factorization of a queried substring range quickly.
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| 今後の研究の推進方策 |
We continue our investigation in processing and managing vast amounts of data arising in bioinformatics, thanks to the proliferation of low-cost sequencing technology. Having established some theoretical background for compression techniques during the previous fiscal year, and introduced practical applications of the positional Burrows-Wheeler transform within the realm of bioinformatics, we are now delving deeper into the findings we shared at DCC'24 and exploring variations of our problem settings. Our primary focus remains on constructing indexes utilizing the Burrows-Wheeler transform and data compression techniques within compressed spaces. Our main target is the efficient indexing of the data in bioinformatics, which aligns with the goals of our research project. In particular, we are striving towards publishing our WABI'23 paper in a journal, which introduced an FM-index capable of faster pattern matching by incorporating insights from our DCC'22 paper. In this endeavor, we are replacing grammar compression with prefix-free parsing (PFP). Presently, our implementation relies on a plain Burrows-Wheeler transform (BWT), resulting in a larger memory footprint compared to a standard FM-index, albeit with quicker query times. Switching to run-length compression and fine-tuning the parameters of PFP should lead to significant improvements in memory utilization. Additionally, we are expanding upon our findings from DCC'24 concerning the computation of LZ78 derivatives from suffix trees to compressed indexes.
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