TY - GEN

T1 - Computing the rooted triplet distance between phylogenetic networks

AU - Jansson, Jesper Andreas

AU - Mampentzidis, Konstantinos

AU - Rajaby, Ramesh

AU - Sung, Wing Kin

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 N1 = (V1,E1) and N2 = (V2,E2) are rooted phylogenetic networks over a common leaf label set of size λ, that Ni has level ki and maximum in-degree i ϵ {1, 2}, for n = max(|V1|, |V2|), m = max(|E1|, |E2|), k = max(k1, k2), and d = max(d1, d2). Previous work has shown how to compute the rooted triplet distance between N1 and N2 in O(λ log λ) 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(n7λ3) 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(n2m + λ3) and O(m + k3d3λ + λ3), 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.

AB - 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 N1 = (V1,E1) and N2 = (V2,E2) are rooted phylogenetic networks over a common leaf label set of size λ, that Ni has level ki and maximum in-degree i ϵ {1, 2}, for n = max(|V1|, |V2|), m = max(|E1|, |E2|), k = max(k1, k2), and d = max(d1, d2). Previous work has shown how to compute the rooted triplet distance between N1 and N2 in O(λ log λ) 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(n7λ3) 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(n2m + λ3) and O(m + k3d3λ + λ3), 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.

UR - http://www.scopus.com/inward/record.url?scp=85069690271&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-25005-8_24

DO - 10.1007/978-3-030-25005-8_24

M3 - Conference article published in proceeding or book

AN - SCOPUS:85069690271

SN - 9783030250041

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 290

EP - 303

BT - Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings

A2 - Colbourn, Charles J.

A2 - Grossi, Roberto

A2 - Pisanti, Nadia

PB - Springer-Verlag

T2 - 30th International Workshop on Combinatorial Algorithms, IWOCA 2019

Y2 - 23 July 2019 through 25 July 2019

ER -