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 general...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 130; pp. 43 - 70
Main Authors: Deng, Shichuan, Li, Jian, Rabani, Yuval
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2022
Subjects:
Approximation algorithms
Clustering
Dynamic points
Facility location
Multi-objective optimization
Facility location
Approximation algorithms
Multi-objective optimization
Clustering
Dynamic points
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2022.07.001