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Sand A, Holt MK, Johansen J, et al. Algorithms for computing the triplet and quartet distances for binary and general trees. Biology (Basel). 2013;2(4):1189-209doi: 10.3390/biology2041189.
Sand, A., Holt, M. K., Johansen, J., Fagerberg, R., Brodal, G. S., Pedersen, C. N., & Mailund, T. (2013). Algorithms for computing the triplet and quartet distances for binary and general trees. Biology, 2(4), 1189-209. https://doi.org/10.3390/biology2041189
Sand, Andreas, et al. "Algorithms for computing the triplet and quartet distances for binary and general trees." Biology vol. 2,4 (2013): 1189-209. doi: https://doi.org/10.3390/biology2041189
Sand A, Holt MK, Johansen J, Fagerberg R, Brodal GS, Pedersen CN, Mailund T. Algorithms for computing the triplet and quartet distances for binary and general trees. Biology (Basel). 2013 Sep 26;2(4):1189-209. doi: 10.3390/biology2041189. PMID: 24833220; PMCID: PMC4009797.
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Biology (Basel). 2013 Sep 26;2(4):1189-209. doi: 10.3390/biology2041189.

Algorithms for computing the triplet and quartet distances for binary and general trees.

Biology

Andreas Sand, Morten K Holt, Jens Johansen, Rolf Fagerberg, Gerth Stølting Brodal, Christian N S Pedersen, Thomas Mailund

Affiliations

  1. Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. [email protected].
  2. Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. [email protected].
  3. Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. [email protected].
  4. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. [email protected].
  5. Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. [email protected].
  6. Department of Computer Science, Aarhus University, IT-Parken, Aabogade 34, DK-8200 Aarhus N, Denmark. [email protected].
  7. Bioinformatics Research Centre, Aarhus University, C.F. Møllers Allé 8, DK-8000 Aarhus C, Denmark. [email protected].

PMID: 24833220 PMCID: PMC4009797 DOI: 10.3390/biology2041189

Abstract

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 counte dimplicitly, 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 oncoloring leaves in one tree and updating a hierarchical decomposition of the other.

References

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