Locating a Tree in a Phylogenetic Network in Quadratic Time

Philippe Gambette, Andreas D. M. Gunawan, Anthony Labarre, Stéphane Vialette, Louxin Zhang

(Submitted on 11 Feb 2015)

A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable phylogenetic networks. We also show that the number of reticulations in a reticulation visible or nearly stable phylogenetic network is bounded from above by a function linear in the number of taxa.