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arXiv · 1411.6804

Reconstructing phylogenetic level-1 networks from nondense binet and trinet sets

Katharina Huber·Leo van Iersel·Vincent Moulton·Celine Scornavacca·Taoyang Wu
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Abstract

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set $\mathcal{T}$ of binary binets or trinets over a set $X$ of taxa, and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an $O(3^{|X|} poly(|X|))$ time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks.

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Katharina Huber, Leo van Iersel, Vincent Moulton, Celine Scornavacca, Taoyang Wu. 2014-11-25. Reconstructing phylogenetic level-1 networks from nondense binet and trinet sets. https://arxiv.org/abs/1411.6804

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