| Summary: | 碩士 === 國立暨南國際大學 === 資訊工程學系 === 98 === The evolutionary tree is an important topic in bioinformation. In 2006, Chen and Lindsay proposed a new method to build the mixture tree from DNA sequences. Mixture tree is an evolutionary tree, and it has two information. One of the information is time parameter, and the other is the set of mutated sites. In 2008, Lin and Juan proposed an algorithm to compute the distance between two mixture trees. Their algorithm computes the distance with only considering the time parameter between two mixture trees. In this work, we proposes three methods to measure the similarity of two mixture trees with considering the set of mutated sites and develop algorithms to compute the distance between two mixture trees.
In this thesis, we give three new definitions of distance, called mutated distance, simple mutated distance, and total mutated distance between two mixture trees by considering the set of mutated sites. For mutated distance, we give three algorithms to compute the mutated distance between two mixture trees. The time complexity are O(n2MaxHeight(T1, T2)), O(n2MaxHeight(T1, T2)) and O(n2), respectively. Where MaxHeight(T1, T2) is the maximum height of tree T1 and T2. For simple mutated distance, we design two algorithms. The time complexity are O(nlogn) and O(n), respectively. Finally, we think that the total mutated number of each site in every path between root and leaf can be used to compute the distance between two mixture trees, so we define the total mutated distance, and design an algorithm for total mutated distance in O(n).
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