On Determining if Tree-based Networks Contain Fixed Trees.

Maria AnayaOlga Anipchenko-UlajAisha AshfaqJoyce ChiuMahedi KaiserMax Shoji OhsawaMegan OwenElla PavlechkoKatherine St JohnShivam SuleriaKeith ThompsonCorrine Yap

Published in: Bulletin of mathematical biology (2016)

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is [Formula: see text]-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-parameter tractable.

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