Steven Kelk and
Celine Scornavacca. Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable. In ALG, Vol. 68(4):886-915, 2014. Keywords: explicit network, FPT, from clusters, level k phylogenetic network, phylogenetic network, phylogeny, reconstruction. Note: http://arxiv.org/abs/1108.3653.
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"Here we show that, given a set of clusters C on a set of taxa X, where |X|=n, it is possible to determine in time f(k)×poly(n) whether there exists a level-≤k network (i.e. a network where each biconnected component has reticulation number at most k) that represents all the clusters in C in the softwired sense, and if so to construct such a network. This extends a result from Kelk et al. (in IEEE/ACM Trans. Comput. Biol. Bioinform. 9:517-534, 2012) which showed that the problem is polynomial-time solvable for fixed k. By defining "k-reticulation generators" analogous to "level-k generators", we then extend this fixed parameter tractability result to the problem where k refers not to the level but to the reticulation number of the whole network. © 2012 Springer Science+Business Media New York."
@Article{KelkScornavacca2014,
AUTHOR = {Kelk, Steven and Scornavacca, Celine},
TITLE = {Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable},
YEAR = {2014},
JOURNAL = {ALG},
VOLUME = {68},
NUMBER = {4},
PAGES = {886-915},
URL = {http://dx.doi.org/10.1007/s00453-012-9708-5},
NOTE = { http://arxiv.org/abs/1108.3653},
KEYWORDS = {explicit network, FPT, from clusters, level k phylogenetic network, phylogenetic network, phylogeny, reconstruction} }
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