在本論文中，我們介紹並研究一個考量非重疊反轉距離(Non-overlapping Inversion Distance)的近似字串比對問題(Approximate String Matching Problem)。給一個內文t、樣版p和一個非負整數k，這個問題的目標是要去找出內文t中所有子字串的位置使得每一個子字串最多使用k個非重疊反轉(Non-overlapping Inversions)轉換成樣版p。首先，我們利用動態規劃(Dynamic Programming)的方法設計出一個演算法可以在O(nm^2 )時間且O(m^2)空間內解決這個問題，其中n是內文的長度，而m是樣版的長度。接著，我們利用一個有效率的篩選策略(Filtering Strategy)提出另一個演算法，這個演算法的時間與空間複雜度皆與我們提出的第一個演算法相同。

In this thesis, we introduce and study the approximate string matching problem under non-overlapping inversion distance. Given a text t, a pattern p and a non-negative integer k, the goal of the problem is to find all locations in the text t that match the pattern p with at most k non-overlapping inversions. First, we use the dynamic programming approach to design an algorithm that solves this problem in O(nm^2 ) time and O(m^2) space, where n is the length of the text and m is the length of the pattern. Next, we present another algorithm based on an efficient filtering strategy that has the same worst-case time and space complexities as the first algorithm.

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