FM-index被廣泛地應用於基因體的序列比對中，它是基於Burrows-Wheeler轉換的資料結構，當基因體有參考序列時，先將參考序列做Burrows-Wheeler轉換後，它便可以快速地將基因片段比對至參考序列上，但它需要額外的空間來儲存比對用的輔助資訊，所需的空間與參考序列的大小呈正比，且大部分的基因體是由上千萬甚至上億個鹼基所組成，因此它所需要的儲存空間會是一大瓶頸。

Ferragina和 Manzini描述了一種FM-index變體的應用，它藉由只儲存部分的輔助資訊和壓縮的轉換後參考序列來減少所需的儲存空間，但是比對一個片段需要數次的解壓縮以及計算的步驟，會導致比對運行時間大幅地增加。

因此我們提出了兩種針對基因序列的壓縮演算法，並將它們應用在FM-index變體上。它們除了可以達到良好的壓縮率外，還能夠在序列壓縮的情況下進行基因比對，省去解壓縮的步驟，進而減少所需的運行時間。此外，我們也嘗試將演算法應用於書籍上，並對它們做字串的比對，結果顯示，同樣能達到高壓縮率以及能夠快速地比對字串。

The FM-index which is based on Burrows–Wheeler transform is broadly used for sequence alignment against DNA sequences. When the reference sequence of a genome exists, the FM-index can efficiently align reads to the reference sequence. However, it requires extra space to store the auxiliary information for alignment. In addition, the required storage space is related to the size of the reference sequence, and since most of the sequences consist of more than tens of millions of nucleobases, the space required for the FM-index would be an issue.

Ferragina and Manzini have described a variant implementation of the FM-index to solve this problem by only storing part of the auxiliary information and the compressed transformed reference sequence. Nevertheless, it requires numbers of decompression and calculation steps to align one read, which results in a significant increase in the computational cost.

Given the above reason, we propose two compression algorithms for DNA sequences and implement them on the variant implementation of the FM-index. Both of the proposed algorithms could effectively reduce the required space, and furthermore, they allow performing sequence alignment with the compressed sequence, which could eliminate the steps of decompression and thereby reducing the computation time. Apart from DNA sequences, we have done pattern matching against publications, and the results show that our algorithms also have a good effect on them.

Chapter 1. Introduction ........................... 1
Chapter 2. Background and Motivation .............. 3
2.1 Burrows–Wheeler transform ..................... 3
2.2 FM-index ...................................... 4
2.3 Variant implementation of the FM-index ........ 5
2.4 Motivation .................................... 6
Chapter 3. Proposed Compression Algorithms .........7
3.1 Overview ...................................... 7
3.2 Modified Run-Length Encoding .................. 7
3.3 Modified Huffman coding with RLE .............. 10
Chapter 4. Experimental Studies ....................13
4.1 Experimental Setup ............................ 13
4.2 Detail Result ................................. 15
4.3 Other Applications ............................ 19
Chapter 5. Conclusion ............................. 24
References ......................................... 25

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