Approximation Algorithms for Clustering with Dynamic Points

We study two generalizations of classic clustering problems called dynamic ordered \(k\)-median and dynamic \(k\)-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between consecutive time steps. In these dynamic clustering problems, the...

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Vydáno v:arXiv.org
Hlavní autoři: Deng, Shichuan, Li, Jian, Rabani, Yuval
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 25.07.2022
Témata:
Algorithms
Approximation
Clients
Clustering
Mathematical analysis
Metric space
Outliers (statistics)
ISSN:2331-8422
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Shrnutí:We study two generalizations of classic clustering problems called dynamic ordered \(k\)-median and dynamic \(k\)-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between consecutive time steps. In these dynamic clustering problems, the general goal is to minimize certain combinations of the service cost of points and the movement cost of centers, or to minimize one subject to some constraints on the other. We obtain a constant-factor approximation algorithm for dynamic ordered \(k\)-median under mild assumptions on the input. We give a 3-approximation for dynamic \(k\)-supplier and a multi-criteria approximation for its outlier version where some points can be discarded, when the number of time steps is two. We complement the algorithms with almost matching hardness results.
Bibliografie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2006.14403