Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the network class ideal for capturing evolutionary histories that involve horizontal gene transfers. Here, we study the minimum number of additional leaves needed to make a network orchard. We demonstrate that computing this proximity measure for a given network is NP-hard. We also give an equivalent measure based on vertex labellings to construct a mixed integer linear programming formulation. Our experimental results, which include both real-world and synthetic data, illustrate the effectiveness of our implementation.

翻译：系统发育网络用于表示物种的进化历史。近年来，新提出的果园网络类被证明可解释为带有附加水平弧的树，这使得该类网络非常适合捕捉涉及水平基因转移的进化历史。本文研究了使网络成为果园网络所需的最小附加叶子节点数量。我们证明，计算给定网络的这一邻近度度量是NP难的。同时，我们基于顶点标记给出了等价度量，并构建了混合整数线性规划公式。包含真实世界与合成数据在内的实验结果表明了我们实现方法的有效性。