On the compatibility of quartet trees

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Phylogenetic tree reconstruction is a fundamental biological problem. Quartet trees, trees over four species, are the minimal informational unit for phylogenetic classification. While every phylogenetic tree over n species defines (n4) quartets, not every set of quartets is compatible with some phylogenetic tree. Here we focus on the compatibility of quartet sets. We provide several results addressing the question of what can be inferred about the compatibility of a set from its subsets. Most of our results use probabilistic arguments to prove the sought characteristics. In particular we show that there are quartet sets Q of size m = cn log n in which every subset of cardinality c'n/ log n is compatible, and yet no fraction of more than 1/3 + ε of Q is compatible. On the other hand, in contrast to the classical result stating when Q is the densest, i.e. m = (n4) the consistency of any set of 3 quartets implies full consistency, we show that even for m = Θ((n4)) there are (very) inconsistent sets for which every subset of large constant cardinality is consistent. Our final result, relates to the conjecture of Bandelt and Dress regarding the maximum quartet distance between trees. We provide asymptotic upper and lower bounds for this value.

Original languageEnglish
Title of host publicationProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
PublisherAssociation for Computing Machinery
Number of pages11
ISBN (Print)9781611973389
StatePublished - 2014
Event25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States
Duration: 5 Jan 20147 Jan 2014

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Country/TerritoryUnited States
CityPortland, OR

ASJC Scopus subject areas

  • Software
  • General Mathematics


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