多重序列排列是計算生物學上一個很重要的課題，如幫助預測蛋白質二級結構，演化樹的分析，在多個序列找出共有的功能，結構等。但是多重序列排列的問題複雜度卻令人沮喪。如果用動態程式規畫比較兩個長度皆為n的序列所需的時間是和n的平方成常數正比的；而比較k個長度皆為n的序列所需的時間則和n的k次方成常數正比。
在這篇論文上，我們提出了一個把各別的序列排列做排列的方法，而且也提出了一個根據序列的相似度來做叢集分類的方法。根據我們的實驗結果，在相似的序列上我們的方法所排列出來的結果比 Clustal W 這個程式還好，執行時間更快。

The multiple sequence alignment (MSA) is a fundamental technique of molecular biology. Biological sequences are aligned with each other vertically in order to show the similarities and differences among them. Due to its importance, many algorithms have been proposed. With dynamic programming, finding the optimal alignment for a pair of sequences can be done in O(n2) time, where n is the length of the two strings. Unfortunately, for the general optimization problem of aligning k sequences of length n , O(nk) time is required.
In this thesis, we shall first propose an efficient group alignment method to perform the alignment between two groups of sequences. Then we shall propose a clustering method to build the tree topology for merging. The clustering method is based on the concept that the two sequences having the longest distance should be split into two clusters. By our experiments, both the alignment quality and required time of our algorithm are better than those of NJ (neighbor joining) algorithm and Clustal W algorithm.

TABLE OF CONTENTS
Page
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Multiple Sequence Alignment . . . . . . . . . . . . . . . . . 4
2.1 Multiple sequence Alignment Problem . . . . . . . . . . . . . . . . . 4
2.2 Scoring Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 A±ne Gap Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Complexity of Multiple Sequence Alignment . . . . . . . . . . . . . . 14
Chapter 3. Previous Algorithms . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Tree Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Star Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Progressive Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 4. The Clustering Method for Multiple Sequence Alignment 22
Chapter 5. Experiment Results and Performance Analysis . . . . . . 35
Chapter 6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Appendixes
Page
A. Blosum Score Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 47
B. PAM Score Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C. Gonnet Score Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 68
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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