Building a small and informative phylogenetic supertree

Jesper Andreas Jansson, Konstantinos Mampentzidis, Sandhya Thekkumpadan Puthiyaveedu

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review


We combine two fundamental, previously studied optimization problems related to the construction of phylogenetic trees called maximum rooted triplets consistency (MAXRTC) and minimally resolved supertree (MINRS) into a new problem, which we call q-maximum rooted triplets consistency (q-MAXRTC). The input to our new problem is a set R of resolved triplets (rooted, binary phylogenetic trees with three leaves each) and the objective is to find a phylogenetic tree with exactly q internal nodes that contains the largest possible number of triplets from R. We first prove that q-MAXRTC is NP-hard even to approximate within a constant ratio for every fixed q ≥ 2, and then develop various polynomial-time approximation algorithms for different values of q. Next, we show experimentally that representing a phylogenetic tree by one having much fewer nodes typically does not destroy too much triplet branching information. As an extreme example, we show that allowing only nine internal nodes is still sufficient to capture on average 80% of the rooted triplets from some recently published trees, each having between 760 and 3081 internal nodes. Finally, to demonstrate the algorithmic advantage of using trees with few internal nodes, we propose a new algorithm for computing the rooted triplet distance between two phylogenetic trees over a leaf label set of size n that runs in O(qn) time, where q is the number of internal nodes in the smaller tree, and is therefore faster than the currently best algorithms for the problem (with O(n log n) time complexity [SODA 2013, ESA 2017]) whenever q = o(log n).

Original languageEnglish
Title of host publication19th International Workshop on Algorithms in Bioinformatics, WABI 2019
EditorsKatharina T. Huber, Dan Gusfield
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771238
Publication statusPublished - Sept 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


  • Approximation algorithm
  • Phylogenetic tree
  • Rooted triplet
  • Supertree

ASJC Scopus subject areas

  • Software


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