Arboreal networks are multi-rooted phylogenetic networks whose underlying graph is a tree. We give an encoding of stack-free arboreal networks in terms of triplets and the novel concept of a duet. This yields a polynomial time algorithm to construct these networks from complete triplet and duet systems. The classification results show correctness and lead to a natural metric on these multi-rooted networks.

翻译：树状网络是一类多根系统发育网络，其底层图结构为树。我们基于三元组和新型“二重奏”概念给出了无栈树状网络的编码方法，从而提出了一个多项式时间算法，可从完整的三元组和二重奏系统构建此类网络。分类结果证明了正确性，并为此类多根网络引入了一种自然度量。