鑒於基因重組問題的重要性益增，Ta等人於2015年定義了非重疊反轉與轉位距離問題，並提出O(n^3)時間之方法。目的為計算兩長度皆為n的字串之突變距離，允許的突變為不互相重疊的反轉與轉位。本論文應用非重疊轉位與run之關聯，提出有效率之方法於O(n^2)時間計算非重疊反轉與轉位距離。

Reacting to the growing interest in large-scale mutation events, Ta et al. introduced the non-overlapping inversion and transposition distance problem in 2015, which is to calculate the mutation distance between two strings of the same length n. The allowed operations include non-overlapping inversions and transpositions. They presented an algorithm with O(n^3) time. In this thesis, we propose an efficient algorithm to solve the same problem in O(n^2) time. Our algorithm depends on a strong connection between the non-overlapping transposition and the run structure.

論文審定書 　i
THESIS VERIFICATION FORM 　ii
論文公開授權書 　iii
謝　辭 　iv
摘　要 　v
ABSTRACT 　vi
LIST OF FIGURES 　viii
Chapter 1. Introduction 　1
Chapter 2. Preliminaries 　4
2.1 The Non-overlapping Inversion and Transposition Distance Problem 　4
2.2 Ta's Algorithm for the Non-overlapping Inversion and Transposition Distance Problem 　5
2.3 Repetitions and Runs 　8
Chapter 3. Our Algorithm 　11
3.1 Computation Overview of the Non-overlapping Inversion and Transposition Distance 　11
3.2 Computation of Equality and Inversion Matrices 　15
3.3 Computation of the Transposition Matrix with a Brute-Force Method 　16
3.4 An Analysis of the Brute-Force Method 　21
3.5 An Improved Method for Computing the Transposition Matrix 　24
Chapter 4. Conclusion 　33
BIBLIOGRAPHY 　34

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