Approximation algorithms for clustering with dynamic points

Shichuan Deng*, Jian Li, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageAmerican English
Pages (from-to)43-70
Number of pages28
JournalJournal of Computer and System Sciences
StatePublished - Dec 2022

Bibliographical note

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© 2022 Elsevier Inc.


  • Approximation algorithms
  • Clustering
  • Dynamic points
  • Facility location
  • Multi-objective optimization


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