Phylogenetic trees are unable to represent the evolutionary process for a collection of species if reticulation events happened, and a generalized model named phylogenetic network was introduced consequently. However, the representation of the evolutionary process for one gene is actually a phylogenetic tree that is “contained” in the phylogenetic network for the considered species containing the gene. Thus a fundamental computational problem named Tree Containment problem arises, which asks whether a phylogenetic tree is contained in a phylogenetic network. The previous research on the problem mainly focused on its rooted version of which the considered tree and network are rooted, and several algorithms were proposed when the considered network is binary or structure-restricted. There is almost no algorithm for its unrooted version except the recent fixed-parameter algorithm with runtime $O(4^kn^2)$ , where $k$ and $n$ are the reticulation number and size of the considered unrooted binary phylogenetic network $N$ , respectively. As the runtime is a little expensive when considering big values of $k$ , we aim to improve it and successfully propose a fixed-parameter algorithm with runtime $O(2.594^kn^2)$ in the paper. Additionally, we experimentally show its effectiveness on biological data and simulated data.

中文翻译：

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无根系统发育网络树包含问题的改进固定参数算法

如果发生网状事件，系统发育树无法代表物种集合的进化过程，因此引入了名为系统发育网络的广义模型。然而，一个基因进化过程的表示实际上是一个系统发育树，它“包含”在包含该基因的所考虑物种的系统发育网络中。因此出现了一个称为树包含问题的基本计算问题，它询问系统发育树是否包含在系统发育网络中。以前对该问题的研究主要集中在其有根版本，即所考虑的树和网络是有根的，并且当所考虑的网络是二元或结构受限时提出了几种算法。$O(4^kn^2)$ ， 在哪里$k$和$n$是所考虑的无根二元系统发育网络的网状数量和大小$N$ ， 分别。由于在考虑大值时运行时有点昂贵$k$ ，我们的目标是对其进行改进并成功提出具有运行时的固定参数算法$O(2.594^kn^2)$在论文中。此外，我们通过实验证明了它对生物数据和模拟数据的有效性。