Computing Refined Buneman Trees in Cubic Time

Gerth Stølting Brodal
Rolf Fagerberg
Anna Östlin
Christian N. S. Pedersen
S. Srinivasa Rao

December 2002


Reconstructing the evolutionary tree for a set of $n$ species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of $O(n^5)$ and a space consumption of $O(n^4)$. In this paper, we present an algorithm with running time $O(n^3)$ and space consumption $O(n^2)$

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