在本論文中，我們首先提出兩個有效率的字串比對演算法，字串比對問題是要找出一個字串P在另一個較長的字串T中所有出現的位置。我們提出的演算法是當P與T的某一子字串在進行比對時，使用最佳的字元比對順序，使得能夠有效率的搜尋P在T中的位置。而找出最佳的字元比對順序，我們使用了分支定界法(Branch and Bound)。我們提出的演算法能夠與其它的字串比對演算法相結合，改進搜尋速度。根據實驗數據，與其它有效率的字串比對演算法比較時，我們提出的演算法能夠有最少的字元比對次數，且在時間上也是有效率的。
論文的第二部分，我們提出了一個過濾式的演算法以及混合過濾式的演算法解決近似字串比對問題，近似字串比對問題是要在一個較長的字串T中找出所有的位置i，其都存在某個T的子字串，結尾位置在i且與P的編輯距離(edit distance)小於或等於一個容錯值k，此問題也稱為k-difference問題。根據實驗數據，對於DNA序列的近似字串比對問題，我們的過濾式演算法比其它的過濾式演算法能夠刪除較多不可能是答案的位置，且我們的混合過濾式的演算法能再進一步的改進過濾效果。
論文的第三部分，我們提出了一個漸進式的演算法來解決DNA重序問題，DNA重序的其中一個目的，是要知道一條未完成組序的DNA序列X與另外一條完整的參考序列R是否相近，且差異點為何，我們可經由新一代的定序儀器得到X的短序列，把這些短序列貼回參考序列R上，以觀察異同點，因此這是一個近似字串比對問題的應用，我們提出了一個漸進式的演算法，其能使用低的錯誤允許值將X短序列貼回R，而也能解決掉無法貼到差異度大的區域問題。

In this thesis, we first propose two algorithms for exact string matching problem, which aims to find all the positions i's in a given text where a given pattern occurs. Our algorithms find an optimal selective comparing order of the characters of the pattern so that we could have a better performance in the searching phase. To find the optimal comparing order, we adopt the branch and bound approach. Moreover, our proposed algorithm can be combined with other existing exact string matching algorithms to improve the searching efficiency. The experimental results show that our algorithms indeed have the smallest number of character comparisons and are also efficient in time as compared with other existing exact string matching algorithms.
Second, we propose a new filtration algorithm, as well as a hybrid filtration strategy, to efficiently solve the approximate string matching problem (also called the k-difference problem), which aims to find all the positions i's in a given text such that there exists a substring of the text ending at position i whose edit distance from a given pattern is less than or equal to a given error bound k. Our experimental results on simulated datasets of DNA sequences show that when compared with other filtration algorithms, our filtration algorithm has better performance on the efficiency to filter out those positions of the text at which the pattern does not occur approximately. Moreover, our hybrid filtration strategy further improves the effectiveness of our filtration algorithm.
Third, we propose a progressive approach to solve the DNA resequencing problem which is defined as follows: We are given an unknown DNA sequence X and a known reference sequence R. Our task is to see whether X and R are similar or not. The present popular approach is to break up X into subsequences by the next generation sequencing (NGS) technologies, called reads. We then map the reads of X onto R with a suitable error bound. However, if the similarity between X and R is not very high (<95%), there would be many reads unmapped, and we then cannot obtain the mutations inside the unmapped regions. One can use a large error bound to increase the number of reads mapped. But it is not a good solution because increasing error bound will also increase the probability of false positive mapping. Our approach uses a small error bound and to increase the number of reads mapped, our approach modifies R each time after the reads are mapped. Thus our approach is a progressive approach. Compared with other available tools, our approach allows us to be able to map more reads to the reference sequence. In our simulated experiments, we also show the high correctness of our mapping algorithm.

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