演化樹是種有根的且葉子有標號的樹，而對於這樹中的每一個內部節點，它有兩個以上的孩子。在計算生物學上，對於給定的一群物種建構一棵演化樹是基本而實在的工作。很不幸地，不同的演算法往往產生不同的演化樹，而即使對於相同的一群物種，不同的研究也有不同的演化結果。因此，如何在這些不同的演化樹上去找到它們的一致性變得非常重要且迫切了。在本篇論文中，我們把焦點放在一系列的一致性問題中最讓人感興趣的一個：尋找最大共同子樹問題（the maximum agreement subtree problem）。
尋找二元樹中最大共同子樹問題定義如下：給定一群其葉子標號在集合L的樹的集合T = { T1, T2, T3, …, Tk } 而其中 T1 是棵二元樹，在L集合上尋找一個最大的卡內基子集使得對於T1, T2, T3, …, Tk 在拓樸學上的限制是同形的。首先，我們會先介紹Bryant的演算法[3]；接著利用支配來改進Bryant的演算法並利用多維的橋式範圍搜尋樹（bridged range search tree）來實作。儘管時間複雜度和最新發表的論文中一樣是O( n2logkn )[15]，但實作上卻比以往的快了許多。

An evolutionary tree is a rooted, leaf-labeled tree. Each internal node of the tree has at least two children. Constructing evolutionary trees for the given species is a fundamental work in computational biology. Unfortunately, different algorithms usually produce different evolutionary trees and different research may have different evolutionary trees even on the same set of the species. It becomes more necessary to know the consensus between those trees recently. We focus on one of the consensus problems and agreement problems: the maximum agreement subtree (MAST) problem.
The MAST problem is as follow : given a set a set T = { T1, T2, T3, …, Tk } of leaf-labeled trees on leaf-labeled set L where T1 is a binary tree, find a maximum cardinality subset X of L such that the topological restrictions of T1, T2, T3, …, Tk are isomorphic. In this paper, we introduce Bryant’s algorithm first and use domination to improve Bryant’s algorithm and implement by bridged range search tree method. Although the time cost is O( (n^2)(logn)^k ), the same to original paper, but the implementation is quicker than before.

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