We combine two fundamental optimization problems related to the construction of phylogenetic trees called maximum rooted triplets consistency and minimally resolved supertree into a new problem, which we call q-maximum rooted triplets consistency (q-MAXRTC). It takes as input a set $\mathcal{R}$ of rooted, binary phylogenetic trees with three leaves each and asks for a phylogenetic tree with exactly q internal nodes that contains the largest possible number of trees from $\mathcal{R}$. We prove that q-MAXRTC is NP-hard to approximate within a constant, develop polynomial-time approximation algorithms for different values of q, and show experimentally that representing a phylogenetic tree by one having much fewer nodes typically does not destroy too much branching information. To demonstrate the algorithmic advantage of using trees with few internal nodes, we also propose a new algorithm for computing the rooted triplet distance that is faster than the existing algorithms when restricted to such trees.

我们将与系统发育树构建相关的两个基本优化问题（称为最大有根三元组一致性和最小解析超树）结合到一个新问题中，我们将其称为q-最大有根三元组一致性（q -MAXRTC）。它以一组作为输入$\mathcal{右}$每个具有三个叶子的有根二元系统发育树，并要求具有恰好q 个内部节点的系统发育树，其中包含最大可能数量的树$\mathcal{右}$。我们证明q -MAXRTC 在常数内是 NP 难逼近的，针对q的不同值开发多项式时间逼近算法，并通过实验证明，用节点少得多的树表示系统发育树通常不会破坏太多分支信息。为了证明使用具有很少内部节点的树的算法优势，我们还提出了一种用于计算有根三元组距离的新算法，当限制于此类树时，该算法比现有算法更快。