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

Biology

Andreas Sand¹  Morten K. Holt¹  Jens Johansen¹  Rolf Fagerberg²  Gerth Stølting Brodal¹  Christian N. S. Pedersen¹ 

[1] Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark; E-Mails:;Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark; E-Mail:

关键词: algorithmic development;    tree comparison;    triplet distance;    quartet distance;   

DOI  :  10.3390/biology2041189

来源: mdpi

【 摘 要 】

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 counted implicitly, 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 on coloring leaves in one tree and updating a hierarchical decomposition of the other.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.