Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees
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, respectivel...
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doaj-d30e0af930834dc9aa81e83c19cb2aa32020-11-24T23:43:11ZengMDPI AGBiology2079-77372013-09-01241189120910.3390/biology2041189Algorithms for Computing the Triplet and Quartet Distances for Binary and General TreesThomas MailundChristian N. S. PedersenRolf FagerbergGerth Stølting BrodalMorten K. HoltJens JohansenAndreas SandDistance 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.http://www.mdpi.com/2079-7737/2/4/1189algorithmic developmenttree comparisontriplet distancequartet distance |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Thomas Mailund Christian N. S. Pedersen Rolf Fagerberg Gerth Stølting Brodal Morten K. Holt Jens Johansen Andreas Sand |
spellingShingle |
Thomas Mailund Christian N. S. Pedersen Rolf Fagerberg Gerth Stølting Brodal Morten K. Holt Jens Johansen Andreas Sand Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees Biology algorithmic development tree comparison triplet distance quartet distance |
author_facet |
Thomas Mailund Christian N. S. Pedersen Rolf Fagerberg Gerth Stølting Brodal Morten K. Holt Jens Johansen Andreas Sand |
author_sort |
Thomas Mailund |
title |
Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees |
title_short |
Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees |
title_full |
Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees |
title_fullStr |
Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees |
title_full_unstemmed |
Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees |
title_sort |
algorithms for computing the triplet and quartet distances for binary and general trees |
publisher |
MDPI AG |
series |
Biology |
issn |
2079-7737 |
publishDate |
2013-09-01 |
description |
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. |
topic |
algorithmic development tree comparison triplet distance quartet distance |
url |
http://www.mdpi.com/2079-7737/2/4/1189 |
work_keys_str_mv |
AT thomasmailund algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT christiannspedersen algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT rolffagerberg algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT gerthstøltingbrodal algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT mortenkholt algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT jensjohansen algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees AT andreassand algorithmsforcomputingthetripletandquartetdistancesforbinaryandgeneraltrees |
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1725502668119474176 |