## Computing the Rooted Triplet Distance between Phylogenetic Networks

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• Jesper Jansson, Department of Computing, The Hong Kong Polytechnic University, Hong Kong
• Konstantinos Mampentzidis
• Ramesh Rajaby, School of Computing, National University of Singapore, Singapore
• Wing-Kin Sung, School of Computing, National University of Singapore, Singapore
The rooted triplet distance measures the structural dissimilarity of two phylogenetic trees or networks by counting the number of rooted trees with exactly three leaf labels that occur as embedded subtrees in one, but not both of them. Suppose that N_1 = (V_1,E_1) and N_2 = (V_2,E_2) are rooted phylogenetic networks over a common leaf label set of size λ, that N_i has level k_i and maximum in-degree d_i for i ∈ {1,2}, and that the networks' out-degrees are unbounded. Denote n = max(|V_1|,|V_2|), m = max(|E_1|,|E_2|), k = max(k_1,k_2), and d = max(d_1, d_2). Previous work has shown how to compute the rooted triplet distance between N_1 and N_2 in O(λlogλ) time in the special case k <= 1. For k > 1, no efficient algorithms are known; a trivial approach leads to a running time of Ω(n^7λ^3) and the only existing non-trivial algorithm imposes restrictions on the networks' in- and out-degrees (in particular, it does not work when non-binary nodes are allowed). In this paper, we develop two new algorithms that have no such restrictions. Their running times are O(n^2m + λ^3) and O(m + k^3d^3λ + λ^3), respectively. We also provide implementations of our algorithms and evaluate their performance in practice. This is the first publicly available software for computing the rooted triplet distance between unrestricted networks of arbitrary levels.
Originalsprog Engelsk Computing the Rooted Triplet Distance between Phylogenetic Networks Charles J. Colbourn, Roberto Grossi, Nadia Pisanti 14 Springer 2019 290-303 978-3-030-25005-8 Udgivet - 2019 30th International Workshop on Combinatorial Algorithms - Computer Science department of the University of Pisa, Pisa, ItalienVarighed: 23 jul. 2019 → 25 jul. 2019http://iwoca2019.di.unipi.it/

### Konference

Konference 30th International Workshop on Combinatorial Algorithms Computer Science department of the University of Pisa Italien Pisa 23/07/2019 → 25/07/2019 http://iwoca2019.di.unipi.it/
Serietitel Theoretical Computer Science and General Issues

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