作用在一個字串S的區段互換(block-interchange)是把S中兩個沒有重疊但未必相鄰的子字串做交換。字首區段互換(prefix block-interchange)是一個特別的區段互換，在兩個互換的子字串中，其中一個子字串必需為整個字串的字首(prefix)。在本論文中，我們研究如何利用字首區段互換對二元字串做排序的問題(sorting by prefix block-interchanges on binary strings)，這個問題的目的是要去找出最少次數的字首區段互換來排序一個二元字串。除此之外，我們也去研究如何計算出兩個二元字串之間的字首區段互換距離(prefix block-interchange distance be-tween binary strings)，這個問題的目的是要去計算出最少次數的字首區段互換來把一個二元字串轉換成另一個二元字串。結果，我們設計出一個線性時間的演算法可以來解決二元字串的字首區段互換排序問題，同時我們也證明了兩個二元子串之間的字首區段互換距離是一個NP-hard問題。

A block-interchange acting on a string 𝑆 exchanges two non-overlapping but not necessary adjacent substrings in 𝑆. A prefix block-interchange is a special block-interchange in which one of the two exchanged substrings is restricted to a prefix of 𝑆. In this thesis, we study the problem of sorting by prefix block-interchanges on binary strings, which is to find the minimum number of prefix block-interchanges to sort a given binary string. In addition, we study the problem of computing the prefix block-interchange distance between two binary strings, which is to compute the minimum number of prefix block-interchanges to transform a given binary string into another given binary string. Consequently, we design a linear-time algorithm to solve the problem of sorting by prefix block-interchange on binary strings and also show that the problem of computing the prefix block-interchange distance between two binary strings is NP-hard.

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