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Time-Optimal k-Server

Authors Fabian Frei , Dennis Komm , Moritz Stocker , Philip Whittington

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LIPIcs.ISAAC.2025.32.pdf
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ACM Subject Classification
  • Theory of computation → K-server algorithms
Keywords
  • k-server problem
  • optimizing time instead of distance
  • deterministic and randomized algorithms
  • Yao’s principle

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Abstract

The time-optimal k-server problem minimizes the time spent instead of the distance traveled when serving n requests, appearing one after the other, with k servers in a metric space. The classical distance model was motivated by a hard disk with k heads. Instead of minimal head movements, the time model aims for optimal reading speeds. 
This paper provides a lower bound of 2k-1 on the competitive ratio of any deterministic online algorithm for the time-optimal k-server problem on a specifically designed metric space. This lower bound coincides with the best known upper bound on the competitive ratio for the classical k-server problem, achieved by the famous work function algorithm. We provide further lower bounds of k+1 for all Euclidean spaces and k for uniform metric spaces. 
Our most technical result, proven by applying Yao’s principle to a suitable instance distribution, is a lower bound of k+H_k-1 that holds even for randomized algorithms, which contrasts with the best known lower bound for the classical problem, which is polylogarithmic in k. 
We hope to initiate further intensive study of this natural problem.

Cite As Get BibTex

Fabian Frei, Dennis Komm, Moritz Stocker, and Philip Whittington. Time-Optimal k-Server. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.32

Author Details

Fabian Frei
  • CSAIL, MIT, Cambridge, MA, USA
Dennis Komm
  • Department of Computer Science, ETH Zürich, Switzerland
Moritz Stocker
  • Department of Computer Science, ETH Zürich, Switzerland
Philip Whittington
  • Department of Computer Science, ETH Zürich, Switzerland

Funding

  • Frei, Fabian: This research was funded in part by grant number 218001 awarded to Fabian Frei by the Swiss National Science Foundation. Work done in part while at CISPA Helmholtz Center for Information Security and ETH Zurich.

Acknowledgements

We thank Peter Rossmanith for his suggestion to study the k-server problem in the time model and Richard Královič for pointing out how the algorithm Robin could be extended to graphs of bounded aspect ratio.

References

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