Abstract
The previous fastest algorithm for computing the rooted triplet distance between two input galled trees (i.e., phylogenetic networks whose cycles are vertex-disjoint) runs in
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$$O ( {n^{2.687}} )$$
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time, where n is the cardinality of the leaf label set. In this article, we present an
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$$O ( n \;{\bf log} \;n )$$
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-time solution. Our strategy is to transform the input so that the answer can be obtained by applying an existing
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$$O ( n \; {\bf log} \;n )$$
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-time algorithm for the simpler case of two phylogenetic trees a constant number of times. The new algorithm has been implemented, and applying it to pairs of randomly generated galled trees with up to
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$$\bf 500 , 000$$
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leaves confirms that it is fast in practice.
