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Fairness in the k-Server Problem

Authors Mohammadreza Daneshvaramoli , Mohammad Hajiesmaili , Shahin Kamali , Helia Karisani , Cameron Musco

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LIPIcs.ITCS.2026.45.pdf
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ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Design and analysis of algorithms
Keywords
  • k-server problem
  • online algorithms
  • fairness
  • competitive analysis

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Abstract

We initiate a formal study of fairness for the k-server problem, where the objective is not only to minimize the total movement cost, but also to distribute the cost equitably among servers. We first define a general notion of (α,β)-fairness, where, for parameters α ≥ 1 and β ≥ 0, no server incurs more than an α/k-fraction of the total cost plus an additive term β. We then show that fairness can be achieved without a loss in competitiveness in both the offline and online settings. In the offline setting, we give a deterministic algorithm that, for any ε > 0, transforms any optimal solution into an (α,β)-fair solution for α = 1 + ε and β = O(diam ⋅ log k / ε), while increasing the cost of the solution by just an additive O(diam ⋅ k log k / ε) term. Here diam is the diameter of the underlying metric space. We give a similar result in the online setting, showing that any competitive algorithm can be transformed into a randomized online algorithm that is fair with high probability against an oblivious adversary and still competitive up to a small loss.
The above results leave open a significant question: can fairness be achieved in the online setting, either with a deterministic algorithm or a randomized algorithm, against a fully adaptive adversary? We make progress towards answering this question, showing that the classic deterministic Double Coverage Algorithm (DCA) is fair on line metrics and on tree metrics when k = 2. However, we also show a negative result: DCA fails to be fair for any non-vacuous parameters on general tree metrics. We further show that on uniform metrics (i.e., the paging problem), the deterministic First-In First-Out (FIFO) algorithm is fair. We show that any "marking algorithm", including the Least Recently Used (LRU) algorithm, also satisfies a weaker, but still meaningful notion of fairness.

Cite As Get BibTex

Mohammadreza Daneshvaramoli, Mohammad Hajiesmaili, Shahin Kamali, Helia Karisani, and Cameron Musco. Fairness in the k-Server Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.45

Author Details

Mohammadreza Daneshvaramoli
  • University of Massachusetts Amherst, MA, USA
Mohammad Hajiesmaili
  • University of Massachusetts Amherst, MA, USA
Shahin Kamali
  • York University, Toronto, Canada
Helia Karisani
  • University of Massachusetts Amherst, MA, USA
Cameron Musco
  • University of Massachusetts Amherst, MA, USA

Funding

This research is supported by National Science Foundation grants 2045641, 2325956, 2512128, and 2533814. And support of the Natural Sciences and Engineering Research Council of Canada (NSERC) funding reference number RGPIN-2025-07295.

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