English

Reconstructing a phylogenetic level-1 network from quartets

Combinatorics 2013-08-26 v1

Abstract

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n^3) time. We also present a more general method which can handle more diverse quartet data, but which takes O(n^6) time. Both methods proceed by solving a certain system of linear equations over GF(2). For a general dense quartet set (containing at least one quartet on every four taxa) our O(n^6) algorithm constructs a phylogenetic level-1 network consistent with the quartet set if such a network exists and returns an (O(n^2) sized) certificate of inconsistency otherwise. This answers a question raised by Gambette, Berry and Paul regarding the complexity of reconstructing a level-1 network from a dense quartet set.

Cite

@article{arxiv.1308.5206,
  title  = {Reconstructing a phylogenetic level-1 network from quartets},
  author = {J. C. M. Keijsper and R. A. Pendavingh},
  journal= {arXiv preprint arXiv:1308.5206},
  year   = {2013}
}
R2 v1 2026-06-22T01:14:10.934Z