TY - JOUR
AU1 - Huber, Katharina
AU2 - Iersel, Leo
AU3 - Moulton, Vincent
AU4 - Scornavacca, Celine
AU5 - Wu, Taoyang
AB - 
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 
$$\mathbb {T}$$


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 of binary binets or trinets over a taxon set X, 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 
$$O(3^{|X|} poly(|X|))$$




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 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.
TI - Reconstructing Phylogenetic Level-1 Networks from Nondense Binet and Trinet Sets
JF - Algorithmica
DO - 10.1007/s00453-015-0069-8
DA - 2015-09-14
UR - https://www.deepdyve.com/lp/springer-journals/reconstructing-phylogenetic-level-1-networks-from-nondense-binet-and-W7dJL7yLsE
SP - 173
EP - 200
VL - 77
IS - 1
DP - DeepDyve
ER -