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Randomized k-Server in Polynomial Time

Authors Christian Coester , Romain Cosson

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LIPIcs.ICALP.2026.65.pdf
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ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → K-server algorithms
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • k-server
  • online algorithms
  • computational complexity
  • randomized complexity
  • advice complexity

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Abstract

We study the design of computationally efficient randomized algorithms for the k-server problem. Existing randomized algorithms with the best known competitive ratios are, on the one hand, inherently implicit and, on the other hand, employ a rounding scheme that maintains a distribution over exponentially many configurations. In this work, we introduce a derandomization framework that transforms any randomized k-server algorithm on a hierarchically separated tree into one that uses only O(log k) random bits for request sequences of arbitrary length - hence maintaining a distribution over only polynomially many server configurations. Leveraging this black-box derandomization, we obtain the first polynomial-time randomized k-server algorithm on arbitrary n-point metrics with a polylogarithmic competitive ratio. Our results also have implications for the advice complexity of the k-server problem.

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Christian Coester and Romain Cosson. Randomized k-Server in Polynomial Time. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.65

Author Details

Christian Coester
  • University of Oxford, UK
Romain Cosson
  • New York University, NY, USA

Funding

  • Coester, Christian: Funded by the European Union (ERC, CCOO, 101165139). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

Acknowledgements

We thank the anonymous reviewers for their constructive feedback.

References

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