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Online k-Median with Consistent Clusters

Authors Benjamin Moseley , Heather Newman , Kirk Pruhs

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Author Details

Benjamin Moseley
  • Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA
Heather Newman
  • Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, USA
Kirk Pruhs
  • Department of Computer Science, University of Pittsburgh, Pittsburgh, PA, USA

Funding

  • Moseley, Benjamin: Supported in part by a Google Research Award, an Inform Research Award, a Carnegie Bosch Junior Faculty Chair, and NSF grants CCF-2121744 and CCF-1845146.
  • Newman, Heather: Supported in part by a Google Research Award, an Inform Research Award, a Carnegie Bosch Junior Faculty Chair, and NSF grants CCF-2121744 and CCF-1845146.
  • Pruhs, Kirk: Supported by NSF grants CCF-1907673, CCF-2036077, CCF-2209654 and an IBM Faculty Award.

Cite As Get BibTex

Benjamin Moseley, Heather Newman, and Kirk Pruhs. Online k-Median with Consistent Clusters. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.20

Abstract

We consider the problem in which n points arrive online over time, and upon arrival must be irrevocably assigned to one of k clusters where the objective is the standard k-median objective. Lower-bound instances show that for this problem no online algorithm can achieve a competitive ratio bounded by any function of n. Thus we turn to a beyond worst-case analysis approach, namely we assume that the online algorithm is a priori provided with a predicted budget B that is an upper bound to the optimal objective value (e.g., obtained from past instances). Our main result is an online algorithm whose competitive ratio (measured against B) is solely a function of k. We also give a lower bound showing that the competitive ratio of every algorithm must depend on k.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • k-median
  • online algorithms
  • learning-augmented algorithms
  • beyond worst-case analysis

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References

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