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**1 - 4**of**4**### The generalized Robinson-Foulds metric

- ALGORITHMS IN BIOINFORMATICS, SPRINGER: US
, 2013

"... The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remo ..."

Abstract
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The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remove the single taxon. To this end, we propose a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration. In contrast to previous approaches, our model requires the matching be-tween clades to respect the structure of the two trees, a property that the classical RF metric exhibits, too. We show that computing this gen-eralized RF metric is, unfortunately, NP-hard. We then present a simple Integer Linear Program for its computation, and evaluate it by an all-against-all comparison of 100 trees from a benchmark data set. We find that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.

### Approximation and parameterized algorithms for common subtrees and edit distance . . .

, 2012

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### Fast alignment of fragmentation trees

"... Motivation: Mass spectrometry allows sensitive, automated and high-throughput analysis of small molecules such as metabolites. One major bottleneck in metabolomics is the identification of ‘unknown ’ small molecules not in any database. Recently, fragmentation tree alignments have been introduced fo ..."

Abstract
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Motivation: Mass spectrometry allows sensitive, automated and high-throughput analysis of small molecules such as metabolites. One major bottleneck in metabolomics is the identification of ‘unknown ’ small molecules not in any database. Recently, fragmentation tree alignments have been introduced for the automated comparison of the fragmentation patterns of small molecules. Fragmentation pattern similarities are strongly correlated with the chemical similarity of the molecules, and allow us to cluster compounds based solely on their fragmentation patterns. Results: Aligning fragmentation trees is computationally hard. Nevertheless, we present three exact algorithms for the problem: a dynamic programming (DP) algorithm, a sparse variant of the DP, and an Integer Linear Program (ILP). Evaluation of our methods on three different datasets showed that thousands of alignments can be computed in a matter of minutes using DP, even for ‘challenging ’ instances. Running times of the sparse DP were an order of magnitude better than for the classical DP. The ILP was clearly outperformed by both DP approaches. We also found that for both DP algorithms, computing the 1 % slowest alignments required as much time as computing the 99 % fastest. Contact: