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arXiv · 2512.03718

Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity

Robert Ganian·Hung P. Hoang·Simon Wietheger
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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.

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Robert Ganian, Hung P. Hoang, Simon Wietheger. 2025-12-03. Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity. https://arxiv.org/abs/2512.03718

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