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 ¿xed 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) certi¿cate 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.

Original language | English |
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Publisher | s.n. |
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Number of pages | 16 |
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Publication status | Published - 2013 |
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Name | arXiv.org |
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Volume | 1308.5206 [math.CO] |
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