Preordering is a generalization of clustering and partial ordering with applications in bioinformatics and social network analysis. Given a finite set $V$ and a value $c_{ab} \in \mathbb{R}$ for every ordered pair $ab$ of elements of $V$, the preordering problem asks for a preorder $\lesssim$ on $V$ that maximizes the sum of the values of those pairs $ab$ for which $a \lesssim b$. Building on the state of the art in solving this NP-hard problem partially, we contribute new partial optimality conditions and efficient algorithms for deciding these conditions. In experiments with real and synthetic data, these new conditions increase, in particular, the fraction of pairs $ab$ for which it is decided efficiently that $a \not\lesssim b$ in an optimal preorder.

翻译：预排序是聚类与偏序关系的推广，在生物信息学和社会网络分析中具有应用。给定有限集 $V$ 及其每一有序元素对 $ab$ 的值 $c_{ab} \in \mathbb{R}$，预排序问题要求在 $V$ 上寻找一个预序 $\lesssim$，使得满足 $a \lesssim b$ 的元素对 $ab$ 的值之和最大化。基于该NP难问题现有部分求解技术，我们提出了新的部分最优性条件及其高效判定算法。在真实与合成数据实验表明，这些新条件特别提高了在最优预序中高效判定 $a \not\lesssim b$ 的元素对 $ab$ 的比例。