FPT approximations for Capacitated Sum of Radii and Diameters
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909773044121600 |
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| author | Filtser, Arnold Gadekar, Ameet |
| author_facet | Filtser, Arnold Gadekar, Ameet |
| contents | The Capacitated Sum of Radii problem involves partitioning a set of points $P$, where each point $p\in P$ has capacity $U_p$, into $k$ clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered at point $p$ is at most $U_p$. We begin by showing that the problem is APX-hard, and that under gap-ETH there is no parameterized approximation scheme (FPT-AS). We then construct a $\approx5.83$-approximation algorithm in FPT time (improving a previous $\approx7.61$ approximation in FPT time). Our results also hold when the objective is a general monotone symmetric norm of radii. We also improve the approximation factors for the uniform capacity case, and for the closely related problem of Capacitated Sum of Diameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | FPT approximations for Capacitated Sum of Radii and Diameters Filtser, Arnold Gadekar, Ameet Data Structures and Algorithms The Capacitated Sum of Radii problem involves partitioning a set of points $P$, where each point $p\in P$ has capacity $U_p$, into $k$ clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered at point $p$ is at most $U_p$. We begin by showing that the problem is APX-hard, and that under gap-ETH there is no parameterized approximation scheme (FPT-AS). We then construct a $\approx5.83$-approximation algorithm in FPT time (improving a previous $\approx7.61$ approximation in FPT time). Our results also hold when the objective is a general monotone symmetric norm of radii. We also improve the approximation factors for the uniform capacity case, and for the closely related problem of Capacitated Sum of Diameters. |
| title | FPT approximations for Capacitated Sum of Radii and Diameters |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.04984 |