單一核苷酸多型性是由於在人體基因中單一個核苷酸改變所造成的。這些單一的核苷酸變異大約每一千個鹼基對就會有一個這樣的現象發生。在這些核苷酸位置上只會有二種可能的核苷酸會顯現出來。由於單一核苷酸多型性序列資料的變異有限加上其資料量十分的豐富，因此很適合拿來當做人類疾病特徵的標誌。
在近期的研究結果中曾指出人類基因體中有區塊狀的結構產生，而且在每個區塊中的變異是有限的。因此，在每個區塊中我們可以利用少部份的單一核苷酸多型性資料來表示這個區塊的變異情形。而這少部份的單一核苷酸多型性資料即被稱之為單一核苷酸多型性標籤。
我們提出了定量變異方法去求得資料內部的變異值。用此方法切割單一核苷酸多型性區塊之後，我們提出一些客觀的評估法來衡量切割的區塊是否恰當。從這個演算法我們求得人類第二十一號染色體的變異值為0.5。切割出來的區塊與NCBI網頁上的haplotype資料有著共同的性質。最後，我們發展標籤篩選演算法去挑選每個區塊中所需要的標籤為何，根據此演算法去挑選標籤我們得到資料壓縮的比率為0.78。

SNP (single nucleotide polymorphisms, pronounce as snip) is one nucleotide position difference within human population.
These differences can be detected in human genome and the difference occurs once about every 1000 base pairs. There are only two possible nucleotides in each SNP position. As a genetic marker, SNP data can be used to capture human disease traits because of its abundance and low diversity.
In recent research results, it has been shown that there is a block-like structure in human genome, and only limited haplotype diversity can be observed. Consequently, we can use only a small fraction of SNPs to capture haplotype diversity in each block, and these SNPs are called tagSNPs.
We propose a fixed-diversity approach to capture the diversity of the entire data. After partitioning the haplotype blocks, we will provide an objective way for evaluating the result. We obtain that the diversity of chromosome 21 SNPs locates at 0.5 by using our algorithm. The partition result shows the concurrence property of the haplotype data downloaded from NCBI web site. Finally, we develop an algorithm for tagSNP selection within each block, and obtain the compression ratio 0.78.

LIST OF FIGURES . . . . . . . . . . . . . . .. . . . . . 4
LIST OF TABLES . . . .. . . . . . . . . . . . . . . . . . 8
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . 1
1.1 Introduction to SNP . . . . . . . . . . . . . . . . . 1
1.2 Characteristics of the Blocks . . . . . . . . . . 4
1.3 The Need of tagSNP Selection . . . . . . . . . . . 5
Chapter 2. Previous Works . . . . . . . . . . . . . . . . 7
2.1 Different Criteria for Block and tagSNP Selection . . 7
2.2 The Fixed-diversity Approach . . . . . . . . . . . . . 9
2.3 The NP-Complete Property . . . . . . . . . . . . . . 11
2.4 SCP Approaches . . . . . . . . . . . . . . . . . . . 12
Chapter 3. Main Ideas . . . . . . . . . . . . . . . . . . 14
3.1 Data Format . . . . . . . . . . . . . . . . . . . . 14
3.2 Problem Definition . . . . . . . . . . . . . . . . . 14
3.3 Diversity Calculation within One Block . . . . . . . 16
3.3.1 Classification . . . . . . . . . . . . . . . . . . 16
3.3.2 Calculation for Diversity . . . . . . . . . . . . . 19
3.4 Setting Fixed-diversity Threshold . . . . . . . . . . 19
Chapter 4. Our Methods . . . . . . . . . . . . . . . . . 20
4.1 Diversity Calculation . . . . . . . . . . . . . . . . 20
4.2 Dealing with Missing Data . . . . . . . . . . . . . . 21
4.2.1 Method 1 . . . . . . . . . . . . . . . . . . . . . 21
4.2.2 Method 2 . . . . . . . . . . . . . . . . . . . . . 24
4.2.3 Method 3 . . . . . . . . . . . . . . . . . . . . . 25
4.2.4 Method 4 . . . . . . . . . . . . . . . . . . . . . 26
4.3 Tag Selection Idea . . . . . . . . . . . . . . . . . 28
Chapter 5. Results and Discussion . . . . . . . . . . . . 31
5.1 The Power of Fixed-diversity Threshold . . . . . . . 31
5.1.1 Random Data Testing . . . . . . . . . . . . . . . 31
5.1.2 Properties of Block Length . . . . . . . . . . . . 32
5.1.3 Implication of Block Number Variance between Diversities . . . . . . . . . . . . . . . . . . . . . . 36
5.1.4 Secondary Block Boundary Effects . . . . . . . . . 38
5.2 Adopting Haplotype Data in Verification . . . . . . 39
5.3 Evaluation of the Partition Results . . . . . . . . 40
5.3.1 Definitions of Penalty Function . . . . . . . . . 40
5.3.2 Statistics of Partition Results . . . . . . . . . 43
5.4 The Number of Required Tags . . . . . . . . . . . . 44
Chapter 6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . 46
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . 47

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