Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial optimization problems in which items may be combined if they are similar. The objective for these problems is to either maximize or minimize the absolute or relative rank of the special subset, with a meta-goal of assessing the robustness of the rank, even in the presence of a well-defined criterion. We classify the computational complexity of all four problems, mostly finding worst-case hardness, then find exact and approximate solutions to special cases and variants of the problems. These structured cases are inspired by several real-world examples and may be used to assess commonly cited facts across disparate domains, as we demonstrate for sources of greenhouse gas emissions that contribute to climate change.

翻译：给定一个无向图表示一组项目之间的相似性，以及一个评估项目的加性度量，我们通过一组组合优化问题来处理某个特殊子集在序数排序中的位置，其中相似的项目可以合并。这些问题的目标是最大化或最小化该特殊子集的绝对或相对排名，其元目标是在即使存在明确准则的情况下评估排名的鲁棒性。我们对所有四个问题的计算复杂度进行了分类，主要在大多数情况下发现了最坏情况下的困难性，然后针对这些问题的特殊情况和变体寻找精确解和近似解。这些结构化案例受到多个现实世界实例的启发，可用于评估跨不同领域中常被引用的事实，正如我们针对导致气候变化的温室气体排放源所展示的那样。