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, 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.
Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. asand@birc.au.dk.
Andreas
A
Sand
Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. the.thawk@gmail.com.
Morten K
MK
Holt
Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. jens.joha@gmail.com.
Jens
J
Johansen
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. rolf@imada.sdu.dk.
Rolf
R
Fagerberg
Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. gerth@cs.au.dk.
Gerth Stølting
GS
Brodal
Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. cstorm@birc.au.dk.
Christian N S
CN
Pedersen
Bioinformatics Research Centre, Aarhus University, C.F. Møllers Allé 8, DK-8000 Aarhus C, Denmark. mailund@birc.au.dk.
Thomas
T
Mailund