如果想用循序搜尋法在文字序列資料庫中找出最相似的序列，是非常耗時的。在過去的研究中，都沒有任何關於循序搜尋法或者其它搜尋順序方法的機率理論分析。因此本論文將以理論的形式來探討，當給定一條查詢序列時，資料庫中的搜尋順序。為了減少搜索空間，我們計算出查詢序列在曼哈頓距離模型上的搜尋機率，以找出下一條需要比較的序列。根據這個搜尋機率，第三條以及之後需要比較的序列都能被決定出來。因此，我們提出了一個搜尋策略⟨0.81, 1⟩來找出最相似的序列，0.81 和1 都分別代表參考序列和查詢序列之間的編輯距離倍數。我們的搜尋策略也利用了編輯距離的三角不等式來加快搜尋速度。透過這種方式，我們的搜尋策略就能把不須比較的序列刪除以加快搜尋的效率。

For finding the most similar sequence in a character-sequence database, it is very time-consuming if the one-by-one sequential search strategy is applied. In the previous studies, there is no theoretical analysis about the probability of the sequential search, or any other order of searching. This thesis studies and theoretically discusses the searching order for a given query sequence in a database. To reduce the searching space, the searching probability for the query sequence on the Manhattan distance model is calculated for selecting the next compared sequence. Accordingly, the third order and the subsequent compared sequences can be determined. Hence, a searching strategy of parameter ⟨0.81, 1⟩ is proposed for finding the most similar sequence, where 0.81 and 1 indicate the multipliers of the edit distance between the reference sequence and the query sequence, respectively. Our searching strategy also considers the triangle inequality of the edit distance for accelerating the searching speed. In this way, our searching strategy can improve the searching efficiency by pruning some unnecessary sequences away.

THESIS VERIFICATION FORM . . . . . . . . . . . . . . . . . . . . . . i
THESIS AUTHORIZATION FORM . . . . . . . . . . . . . . . . . . . . iii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 The Longest Common Subsequence Problem . . . . . . . . . . . . . . 3
2.2 The Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 The Triangle Inequality of the Edit Distance . . . . . . . . . . . . . . 7
2.4 The Lp-norm and Manhattan Distance . . . . . . . . . . . . . . . . . 9
2.5 Finding the Most Similar Sequence in a Character-sequence
Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 3. The Prune-and-Search Algorithm . . . . . . . . . . . . . . 11
3.1 The First Compared Sequence . . . . . . . . . . . . . . . . . . . . . . 11
3.2 The Second Compared Sequence . . . . . . . . . . . . . . . . . . . . . 12
3.2.1 The Intersection of Two Circles . . . . . . . . . . . . . . . . . 13
3.2.2 The Expected Value of the Manhattan Distance Model . . . . 17
3.3 The Third and the Subsequent Sequences . . . . . . . . . . . . . . . . 37
3.4 The Algorithm for the MSS Problem . . . . . . . . . . . . . . . . . . 40
Chapter 4. Experimental Results . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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