{"ID":2833466,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.03718","arxiv_id":"2512.03718","title":"Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity","abstract":"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.","short_abstract":"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 i...","url_abs":"https://arxiv.org/abs/2512.03718","url_pdf":"https://arxiv.org/pdf/2512.03718v1","authors":"[\"Robert Ganian\",\"Hung P. Hoang\",\"Simon Wietheger\"]","published":"2025-12-03T12:07:24Z","proceeding":"cs.DS","tasks":"[\"cs.DS\",\"cs.AI\"]","methods":"[]","has_code":false}