Conference Paper

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

DOI: 10.1142/9781860947995_0013 Conference: Proceedings of 5th Asia-Pacific Bioinformatics Conference, APBC 2007, 15-17 January 2007, Hong Kong, China

Source: DBLP

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**ABSTRACT:**Distance measures between trees are useful for comparing trees in a systematic manner, and several different distance measures have been proposed. The triplet and quartet distances, for rooted and unrooted trees, respectively, are defined as the number of subsets of three or four leaves, respectively, where the topologies of the induced subtrees differ. These distances can trivially be computed by explicitly enumerating all sets of three or four leaves and testing if the topologies are different, but this leads to time complexities at least of the order n3 or n4 just for enumerating the sets. The different topologies can be counte dimplicitly, however, and in this paper, we review a series of algorithmic improvements that have been used during the last decade to develop more efficient algorithms by exploiting two different strategies for this; one based on dynamic programming and another based oncoloring leaves in one tree and updating a hierarchical decomposition of the other.Biology 12/2013; 2(4):1189-209. -
##### 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:**The triplet distance is a distance measure that compares two rooted trees on the same set of leaves by enumerating all sub-sets of three leaves and counting how often the induced topologies of the tree are equal or different. We present an algorithm that computes the triplet distance between two rooted binary trees in time O (n log2n). The algorithm is related to an algorithm for computing the quartet distance between two unrooted binary trees in time O (n log n). While the quartet distance algorithm has a very severe overhead in the asymptotic time complexity that makes it impractical compared to O (n 2) time algorithms, we show through experiments that the triplet distance algorithm can be implemented to give a competitive wall-time running time.BMC Bioinformatics 01/2013; 14(2). · 2.67 Impact Factor

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