Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908691033227264 |
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| author | Ganian, Robert Hoang, Hung P. Wietheger, Simon |
| author_facet | Ganian, Robert Hoang, Hung P. Wietheger, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity Ganian, Robert Hoang, Hung P. Wietheger, Simon Data Structures and Algorithms Artificial Intelligence 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. |
| title | Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity |
| topic | Data Structures and Algorithms Artificial Intelligence |
| url | https://arxiv.org/abs/2512.03718 |