A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

Leo Van Iersel (1) , Steven Kelk (2) , Nela Lekić (2) , Celine Scornavacca (3)

1 CWI - Centrum voor Wiskunde en Informatica
2 Department of data science and Knowledge Engineering [Maastricht]
3 UMR ISEM - Institut des Sciences de l'Evolution de Montpellier

Background: Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Results: Here we present CYCLEKILLER and NONBINARYCYCLEKILLER, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Conclusions: Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TERMINUSEST, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NONBINARYCYCLEKILLER algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

Mots clés: Hybridization number; Phylogenetic networks; Approximation algorithms; Directed feedback vertex set

Domaines: Informatique [cs]; Bio-informatique [q-bio.QM]

Leo Van Iersel, Steven Kelk, Nela Lekić, Celine Scornavacca. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees. BMC Bioinformatics, 2014, 15 (1), pp.296-302. ⟨10.1186/1471-2105-15-127⟩. ⟨hal-02154944⟩