dc.contributor.author | Inamdar, Tanmay Nitin | |
dc.contributor.author | Varadarajan, Kasturi | |
dc.date.accessioned | 2023-02-27T12:57:31Z | |
dc.date.available | 2023-02-27T12:57:31Z | |
dc.date.created | 2023-01-31T10:45:59Z | |
dc.date.issued | 2022 | |
dc.identifier.issn | 1868-8969 | |
dc.identifier.uri | https://hdl.handle.net/11250/3054287 | |
dc.description.abstract | In the Non-Uniform k-Center (NUkC) problem, a generalization of the famous k-center clustering problem, we want to cover the given set of points in a metric space by finding a placement of balls with specified radii. In t-NUkC, we assume that the number of distinct radii is equal to t, and we are allowed to use k_i balls of radius r_i, for 1 ≤ i ≤ t. This problem was introduced by Chakrabarty et al. [ACM Trans. Alg. 16(4):46:1-46:19], who showed that a constant approximation for t-NUkC is not possible if t is unbounded, assuming 𝖯 ≠ NP. On the other hand, they gave a bicriteria approximation that violates the number of allowed balls as well as the given radii by a constant factor. They also conjectured that a constant approximation for t-NUkC should be possible if t is a fixed constant. Since then, there has been steady progress towards resolving this conjecture - currently, a constant approximation for 3-NUkC is known via the results of Chakrabarty and Negahbani [IPCO 2021], and Jia et al. [SOSA 2022]. We push the horizon by giving an O(1)-approximation for the Non-Uniform k-Center for 4 distinct types of radii. Our result is obtained via a novel combination of tools and techniques from the k-center literature, which also demonstrates that the different generalizations of k-center involving non-uniform radii, and multiple coverage constraints (i.e., colorful k-center), are closely interlinked with each other. We hope that our ideas will contribute towards a deeper understanding of the t-NUkC problem, eventually bringing us closer to the resolution of the CGK conjecture. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Dagstuhl Publishing | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Non-Uniform k-Center and Greedy Clustering | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2022 The Author(s) | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | https://doi.org/10.4230/LIPIcs.SWAT.2022.28 | |
dc.identifier.cristin | 2119620 | |
dc.source.journal | Leibniz International Proceedings in Informatics | en_US |
dc.source.pagenumber | 28:1-28:20 | en_US |
dc.identifier.citation | Leibniz International Proceedings in Informatics. 2022, 227, 28:1-28:20. | en_US |
dc.source.volume | 227 | en_US |