A sub-cubic time algorithm for computing the quartet distance between two general trees.
Bottom Line:
When inferring phylogenetic trees different algorithms may give different trees.To study such effects a measure for the distance between two trees is useful.Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees.
Affiliation: Bioinformatics Research Centre (BiRC), Aarhus University, C, F, Møllers Alle 8, DK-8000 Aarhus C, Denmark. jn@birc.au.dk.
ABSTRACT
Background: When inferring phylogenetic trees different algorithms may give different trees. To study such effects a measure for the distance between two trees is useful. Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees. Results: We have derived a new algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree ≥ 3. The time and space complexity of our algorithm is sub-cubic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm so far for computing the quartet distance between general trees independent of the degree of the inner nodes. Conclusions: We have implemented our algorithm and two of the best competitors. Our new algorithm is significantly faster than the competition and seems to run in close to quadratic time in practice. No MeSH data available. |
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Mentions: The crux of the algorithm is to consider each pair of claims, one from each tree, and for each such pair count the number of shared and different directed butterflies claimed in the two trees. This way each shared butterfly is counted twice, and each different butterfly is counted four times, as shown in Figure 4. Dividing the counts by two and four, respectively, gives us sharedB(T, T') and diffB(T, T'). |
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Affiliation: Bioinformatics Research Centre (BiRC), Aarhus University, C, F, Møllers Alle 8, DK-8000 Aarhus C, Denmark. jn@birc.au.dk.
Background: When inferring phylogenetic trees different algorithms may give different trees. To study such effects a measure for the distance between two trees is useful. Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees.
Results: We have derived a new algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree ≥ 3. The time and space complexity of our algorithm is sub-cubic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm so far for computing the quartet distance between general trees independent of the degree of the inner nodes.
Conclusions: We have implemented our algorithm and two of the best competitors. Our new algorithm is significantly faster than the competition and seems to run in close to quadratic time in practice.
No MeSH data available.