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arXiv · 1308.5206

Reconstructing a phylogenetic level-1 network from quartets

J. C. M. Keijsper·R. A. Pendavingh
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Abstract

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n^3) time. We also present a more general method which can handle more diverse quartet data, but which takes O(n^6) time. Both methods proceed by solving a certain system of linear equations over GF(2). For a general dense quartet set (containing at least one quartet on every four taxa) our O(n^6) algorithm constructs a phylogenetic level-1 network consistent with the quartet set if such a network exists and returns an (O(n^2) sized) certificate of inconsistency otherwise. This answers a question raised by Gambette, Berry and Paul regarding the complexity of reconstructing a level-1 network from a dense quartet set.

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J. C. M. Keijsper, R. A. Pendavingh. 2013-08-23. Reconstructing a phylogenetic level-1 network from quartets. https://arxiv.org/abs/1308.5206

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