2025/12/03 by Robert Ganian, Hung P. Hoang, Ganian, Robert +3
Computer Science · Economics, Econometrics and Finance · #Advanced Graph Theory Research #Artificial Intelligence (cs.AI) #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2512.03718
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most k values. While NP-hard in both the fairness-oblivious and the fair settings, the problem is well-known to admit a fixed-parameter algorithm in the former ``vanilla'' setting. As our first contribution, we exclude an analogous algorithm even for highly restricted fair means clustering instances. We then proceed to obtain a full complexity landscape of the problem, and establish tractability results which capture three means of circumventing our obtained lower bound: placing additional constraints on the problem instances, fixed-parameter approximation, or using an alternative parameterization targeting tree-like matrices.