🤖 AI Summary
This study investigates the robustness of subset rankings under ordinal aggregation by merging similar items in an item similarity graph, assuming additive evaluation metrics. The problem is formulated as four classes of combinatorial optimization tasks, aiming to maximize or minimize either the absolute or relative rank of a given subset. The work provides the first systematic characterization of the computational complexity of ranking optimization with partitioning operations, establishing NP-hardness for most variants while developing exact and approximation algorithms tailored to realistic, structured graph topologies. The proposed methodology is successfully applied to assess the robustness of rankings of greenhouse gas emission sources, demonstrating its practical utility across domains.
📝 Abstract
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.