Computing the Quartet Distance Between Evolutionary Trees of Bounded Degree.
01/2007; In proceeding of: Proceedings of 5th Asia-Pacific Bioinformatics Conference, APBC 2007, 15-17 January 2007, Hong Kong, China
- Systematic Biology - SYST BIOL. 01/1993; 42(2):126-141.
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ABSTRACT: Leaf-labelled trees are widely used to describe evolutionary relationships, particularly in biology. In this setting, extant species label the leaves of the tree, while the internal vertices correspond to ancestral species. Various techniques exist for reconstructing these evolutionary trees from data, and an important problem is to determine how "far apart" two such reconstructed trees are from each other, or indeed from the true historical tree. To investigate this question requires tree metrics, and these can be induced by operations that rearrange trees locally. Here we investigate three such operations: nearest neighbour interchange (NNI), subtree prune and regraft (SPR), and tree bisection and reconnection (TBR). The SPR operation is of particular interest as it can be used to model biological processes such as horizontal gene transfer and recombination. We count the number of unrooted binary trees one SPR from any given unrooted binary tree, as well as providing new upper and lower bounds for the diameter of the adjacency graph of trees under SPR and TBR. We also show that the problem of computing the minimum number of TBR operations required to transform one tree to another can be reduced to a problem whose size is a function just of the distance between the trees (and not of the size of the two trees), and thereby establish that the problem is fixed-parameter tractable.Annals of Combinatorics 09/2000; · 0.33 Impact Factor
Conference Proceeding: Computing the Quartet Distance Between Trees of Arbitrary Degree.[show abstract] [hide abstract]
ABSTRACT: We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—sub-trees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the quartet distance between binary trees. In this paper, we present two algorithms for computing the quartet distance between trees of arbitrary degrees. One in time O(n 3) and space O(n 2) and one in time O(n 2 d 2) and space O(n 2), where n is the number of species and d is the maximal degree of the internal nodes of the trees. We experimentally compare the two algorithms and discuss possible directions for improving the running time further.Algorithms in Bioinformatics, 5th International Workshop, WABI 2005, Mallorca, Spain, October 3-6, 2005, Proceedings; 01/2005
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