Parameterized Approximation Algorithms for Sum of Radii Clustering and Variants
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| Title: | Parameterized Approximation Algorithms for Sum of Radii Clustering and Variants |
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| Authors: | Xianrun Chen, Dachuan Xu, Yicheng Xu, Yong Zhang |
| Source: | Proceedings of the AAAI Conference on Artificial Intelligence. 38:20666-20673 |
| Publisher Information: | Association for the Advancement of Artificial Intelligence (AAAI), 2024. |
| Publication Year: | 2024 |
| Description: | Clustering is one of the most fundamental tools in artificial intelligence, machine learning, and data mining. In this paper, we follow one of the recent mainstream topics of clustering, Sum of Radii (SoR), which naturally arises as a balance between the folklore k-center and k-median. SoR aims to determine a set of k balls, each centered at a point in a given dataset, such that their union covers the entire dataset while minimizing the sum of radii of the k balls. We propose a general technical framework to overcome the challenge posed by varying radii in SoR, which yields fixed-parameter tractable (fpt) algorithms with respect to k (i.e., whose running time is f(k) ploy(n) for some f). Our framework is versatile and obtains fpt approximation algorithms with constant approximation ratios for SoR as well as its variants in general metrics, such as Fair SoR and Matroid SoR, which significantly improve the previous results. |
| Document Type: | Article |
| ISSN: | 2374-3468 2159-5399 |
| DOI: | 10.1609/aaai.v38i18.30053 |
| Accession Number: | edsair.doi...........84f9d48ca76bca2bcc73a06a87d4f478 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | Clustering is one of the most fundamental tools in artificial intelligence, machine learning, and data mining. In this paper, we follow one of the recent mainstream topics of clustering, Sum of Radii (SoR), which naturally arises as a balance between the folklore k-center and k-median. SoR aims to determine a set of k balls, each centered at a point in a given dataset, such that their union covers the entire dataset while minimizing the sum of radii of the k balls. We propose a general technical framework to overcome the challenge posed by varying radii in SoR, which yields fixed-parameter tractable (fpt) algorithms with respect to k (i.e., whose running time is f(k) ploy(n) for some f). Our framework is versatile and obtains fpt approximation algorithms with constant approximation ratios for SoR as well as its variants in general metrics, such as Fair SoR and Matroid SoR, which significantly improve the previous results. |
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| ISSN: | 23743468 21595399 |
| DOI: | 10.1609/aaai.v38i18.30053 |