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Biology 2013, 2(4), 1189-1209; doi:10.3390/biology2041189

Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees

Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark
Bioinformatics Research Centre, Aarhus University, C.F. Møllers Allé 8, DK-8000 Aarhus C, Denmark
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
MADALGO - Center for Massive Data Algorithms, a Centre of the Danish National Research Foundation, Aabogade 34, DK-8200 Aarhus N, Denmark
Author to whom correspondence should be addressed.
Received: 15 July 2013 / Revised: 29 August 2013 / Accepted: 13 September 2013 / Published: 26 September 2013
(This article belongs to the Special Issue Developments in Bioinformatic Algorithms)
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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.
Keywords: algorithmic development; tree comparison; triplet distance; quartet distance algorithmic development; tree comparison; triplet distance; quartet distance
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Sand, A.; Holt, M.K.; Johansen, J.; Fagerberg, R.; Brodal, G.S.; Pedersen, C.N.S.; Mailund, T. Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees. Biology 2013, 2, 1189-1209.

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