Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees

Andreas Sand, Morten Kragelund Holt, Jens Johansen, Rolf Fagerberg, Christian Nørgaard Storm Pedersen, Gerth Stølting Brodal, Thomas Mailund

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Distance measures between trees are useful for comparing trees in a systematic
manner, and several different distance measures have been proposed. The triplet and quartet
distances, for rooted and unrooted trees, respectively, are defined as the number of subsets
of three or four leaves, respectively, where the topologies of the induced subtrees differ.
These distances can trivially be computed by explicitly enumerating all sets of three or four
leaves and testing if the topologies are different, but this leads to time complexities at least
of the order n3 or n4 just for enumerating the sets. The different topologies can be counted
implicitly, however, and in this paper, we review a series of algorithmic improvements that
have been used during the last decade to develop more efficient algorithms by exploiting
two different strategies for this; one based on dynamic programming and another based on
coloring leaves in one tree and updating a hierarchical decomposition of the other.
Original languageEnglish
Pages (from-to)1189-1209
Number of pages21
Publication statusPublished - 2013

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