计算有根和无根最大一致超树
Computing Rooted and Unrooted Maximum Consistent Supertrees
摘要：
在遗传学和数据库理论中的一个主要问题是从一组有根树或无根树中计算最大一致树。一个标准的输入是三元组，三叶上的有根二叉树，或四元组，四叶上的无根二叉树。对于m个三元组（四元组）的集合，每个三元组被n个标签的某个子集标记为不同的叶，我们给出了在时间O（2^n^5 m^2 log（m））内构造有根和无根最大一致超树的精确算法。该算法扩展到加权三元组（四元组）。我们进一步提出了在多项式空间中构造有根和无根最大相容树的快速精确算法。最后，对于一个由m棵有根树或无根树组成的集合T，它的最大度为D，并且被n个标号的集合L的某个子集明确地叶标号，我们在O（2^{mD} n^m m^5 n^6 log（m））时间内计算出一棵树，它被L的一个最大尺寸子集X明确地叶标号，T中的所有树，当限制为X时，都与之一致。
英文摘要：
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2^n n^5 m^2 log(m)) for a set of m triplets (quartets), each one distinctly leaf-labeled by some subset of n labels. The algorithms extend to weighted triplets (quartets). We further present fast exact algorithms for constructing rooted and unrooted maximum consistent trees in polynomial space. Finally, for a set T of m rooted or unrooted trees with maximum degree D and distinctly leaf-labeled by some subset of a set L of n labels, we compute, in O(2^{mD} n^m m^5 n^6 log(m)) time, a tree distinctly leaf-labeled by a maximum-size subset X of L that all trees in T, when restricted to X, are consistent with.
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