Efficiently Computing the Robinson-Foulds Metric

Abstract

The Robinson-Foulds (RF) metric is the measure most widely used in comparing phylogenetic trees; it can be computed in linear time using Day's algorithm. When faced with the need to compare large numbers of large trees, however, even linear time becomes prohibitive. We present a randomized approximation scheme that provides, in sublinear time and with high probability, a (1 + epsilon) approximation of the true RF metric. Our approach is to use a sublinear-space embedding of the trees, combined with an application of the Johnson-Lindenstrauss lemma to approximate vector norms very rapidly. We complement our algorithm by presenting an efficient embedding procedure, thereby resolving an open issue from the preliminary version of this paper. We have also improved the performance of Day's (exact) algorithm in practice by using techniques discovered while implementing our approximation scheme. Indeed, we give a unified framework for edge-based tree algorithms in which implementation tradeoffs are clear. Finally, we present detailed experimental results illustrating the precision and running-time tradeoffs as well as demonstrating the speed of our approach. Our new implementation, FastRF, is available as an open-source tool for phylogenetic analysis.

Branch-and-Bound Approach for Parsimonious Inference of a Species Tree from a Set of Gene Family Trees

“…maximizes) this cost and c norm (G, S) the normalized cost over the range of possible values and defined as follows: S min )). The similarity between S and the species tree S 0 is evaluated by the classical Robinson and Foulds distance between phylogenetic trees [15,16], denoted RF (S 0 , S). For the three costs, Figures 3 (left) below depicts the distribution of each tree S ∈ K n according to the normalized cost l norm (G, S).…”

Knowledge-based model for constructing master assembly sequence

“…The Robinson-Foulds (RF) distance [33] is a commonly used metric for matching phylogenetic trees [34]. Given two trees T1 and T2, each contains m number of leaves; then C1 is a set consisting of m − 1 subsets each signifying one of the m − 1 nodes of T1.…”

Adapting simultaneous analysis phylogenomic techniques to study complex disease gene relationships

“…The RF distance between two trees is defined by the sum of the number of data partitions implied by one, but not both, of the trees. A variety of algorithms exist for computing RF distance [76,77], and an optimal method is usually selected on the basis of algorithmic complexity and worst-case running time [51,78,79]. In this study, a gene network was constructed based on tree topology similarity using RF (transformed to RF 0 , which converts RF values onto a scale where higher values correspond to less similarity).…”