Conference Paper

# Computing the Quartet Distance Between Evolutionary Trees of Bounded Degree.

In proceeding of: Proceedings of 5th Asia-Pacific Bioinformatics Conference, APBC 2007, 15-17 January 2007, Hong Kong, China

Source: DBLP

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**ABSTRACT:**We define, analyze, and give efficient algorithms for two kinds of distance measures for rooted and unrooted phylogenies. For rooted trees, our measures are based on the topologies the input trees induce on triplets; that is, on three-element subsets of the set of species. For unrooted trees, the measures are based on quartets (four-element subsets). Triplet and quartet-based distances provide a robust and fine-grained measure of the similarities between trees. The distinguishing feature of our distance measures relative to traditional quartet and triplet distances is their ability to deal cleanly with the presence of unresolved nodes, also called polytomies. For rooted trees, these are nodes with more than two children; for unrooted trees, they are nodes of degree greater than three. Our first class of measures are parametric distances, where there is a parameter that weighs the difference between an unresolved triplet/quartet topology and a resolved one. Our second class of measures are based on Hausdorff distance. Each tree is viewed as a set of all possible ways in which the tree could be refined to eliminate unresolved nodes. The distance between the original (unresolved) trees is then taken to be the Hausdorff distance between the associated sets of fully resolved trees, where the distance between trees in the sets is the triplet or quartet distance, as appropriate. Comment: 34 pages06/2009; -
##### Conference Paper: A Quadratic Time Algorithm for Computing the Quartet Distance between Two General Trees.

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**ABSTRACT:**We derive a quadratic time and space algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree 3. The time and space complexity of our algorithm is quadratic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm for computing the quartet distance between general trees independent of the degree of the inner nodes.International Joint Conferences on Bioinformatics, Systems Biology and Intelligent Computing, IJCBS 2009, Shanghai, China, 3-5 August 2009; 01/2009 - [Show abstract] [Hide abstract]

**ABSTRACT:**When inferring phylogenetic trees different algorithms may give different trees. To study such effects a measure for the distance between two trees is useful. Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees. We have derived a new algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree ≥ 3. The time and space complexity of our algorithm is sub-cubic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm so far for computing the quartet distance between general trees independent of the degree of the inner nodes. We have implemented our algorithm and two of the best competitors. Our new algorithm is significantly faster than the competition and seems to run in close to quadratic time in practice.Algorithms for Molecular Biology 06/2011; 6:15. · 1.61 Impact Factor

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