Computing the quartet distance between trees of arbitrary degree

Authors:
Chris Christiansen;Thomas Mailund;Christian N. S. Pedersen;Martin Randers
Affiliations:
Department of Computer Science, University of Aarhus, Århus N, Denmark;Bioinformatics Research Center, University of Aarhus, Århus C, Denmark;Department of Computer Science, University of Aarhus, Århus N, Denmark;Department of Computer Science, University of Aarhus, Århus N, Denmark
Venue:
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Year:
2005

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Abstract

We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—sub-trees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the quartet distance between binary trees. In this paper, we present two algorithms for computing the quartet distance between trees of arbitrary degrees. One in time O(n3) and space O(n2) and one in time O(n2d2) and space O(n2), where n is the number of species and d is the maximal degree of the internal nodes of the trees. We experimentally compare the two algorithms and discuss possible directions for improving the running time further.