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- W2949161878 abstract "The hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view accurately inferring the location in a phylogenetic tree is notoriously difficult and poor placement can artificially inflate the hybridization number. To this end we study a number of relaxed variants of this problem. We start by showing that the fundamental problem of determining whether an emph{unrooted} phylogenetic network displays (i.e. embeds) an emph{unrooted} phylogenetic tree, is NP-hard. On the positive side we show that this problem is FPT in reticulation number. In the rooted case the corresponding FPT result is trivial, but here we require more subtle argumentation. Next we show that the hybridization number problem for unrooted networks (when given two unrooted trees) is equivalent to the problem of computing the Tree Bisection and Reconnect (TBR) distance of the two unrooted trees. In the third part of the paper we consider the root uncertain variant of hybridization number. Here we are free to choose the location in each of a set of unrooted input trees such that the hybridization number of the resulting rooted trees is minimized. On the negative side we show that this problem is APX-hard. On the positive side, we show that the problem is FPT in the hybridization number, via kernelization, for any number of input trees." @default.
- W2949161878 created "2019-06-27" @default.
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- W2949161878 date "2016-09-02" @default.
- W2949161878 modified "2023-09-27" @default.
- W2949161878 title "On unrooted and root-uncertain variants of several well-known phylogenetic network problems" @default.
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