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A sub-cubic time algorithm for computing the quartet distance between two general trees.

Nielsen J, Kristensen AK, Mailund T, Pedersen CN - Algorithms Mol Biol (2011)

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.

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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.

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.


Counting shared quartets. Graphical illustration of the shared quartet expression, eq. (19). On the left, the matrix entries summed over are explicitly shown. On the right, the inner sum is implicitly shown. The sum of the greyed entries can be computed in constant time.
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Figure 6: Counting shared quartets. Graphical illustration of the shared quartet expression, eq. (19). On the left, the matrix entries summed over are explicitly shown. On the right, the inner sum is implicitly shown. The sum of the greyed entries can be computed in constant time.

Mentions: or the sum of for all distinct entries in I but fixed (i, j), see Figure 6(a). We divide by two since we count each quartet twice, due to symmetry between the (k, l) and (m, n) pairs.


A sub-cubic time algorithm for computing the quartet distance between two general trees.

Nielsen J, Kristensen AK, Mailund T, Pedersen CN - Algorithms Mol Biol (2011)

Counting shared quartets. Graphical illustration of the shared quartet expression, eq. (19). On the left, the matrix entries summed over are explicitly shown. On the right, the inner sum is implicitly shown. The sum of the greyed entries can be computed in constant time.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3141660&req=5

Figure 6: Counting shared quartets. Graphical illustration of the shared quartet expression, eq. (19). On the left, the matrix entries summed over are explicitly shown. On the right, the inner sum is implicitly shown. The sum of the greyed entries can be computed in constant time.
Mentions: or the sum of for all distinct entries in I but fixed (i, j), see Figure 6(a). We divide by two since we count each quartet twice, due to symmetry between the (k, l) and (m, n) pairs.

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.

View Article: PubMed Central - HTML - PubMed

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.