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Token Distribution Revisited

Authors Petra Berenbrink , Robert Elsässer , Tom Friedetzky , Hamed Hosseinpour , Dominik Kaaser

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LIPIcs.DISC.2026.42.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Random walks and Markov chains
Keywords
  • network
  • load balancing
  • discrete
  • token distribution

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Abstract

We consider a well-known model for load balancing called token distribution. Starting from an arbitrary distribution of discrete tokens among the nodes of a network, in each time step the edges of a matching are used to transfer at most one token between matched nodes of unequal load. More precisely, if the difference between two matched nodes is at least two, one (and only one) token is moved from the higher-loaded to the lower-loaded node. If the difference is exactly one, this "excess token" is moved with probability 1/2. We prove that for any initial load vector with discrepancy K, our protocol reaches a discrepancy of two in O(K⋅τ_g⋅log log n) rounds with high probability, where τ_g is the balancing time of the continuous diffusion model.

Cite As Get BibTex

Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Hamed Hosseinpour, and Dominik Kaaser. Token Distribution Revisited. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.42

Author Details

Petra Berenbrink
  • University of Hamburg, Germany
Robert Elsässer
  • University of Salzburg, Austria
Tom Friedetzky
  • Durham University, UK
Hamed Hosseinpour
  • University of Hamburg, Germany
Dominik Kaaser
  • Hamburg University of Technology, Germany

Funding

  • Berenbrink, Petra: Deutsche Forschungsgemeinschaft (DFG) grant 411362735.
  • Elsässer, Robert: Austrian Science Fund (FWF) grant DOI 10.55776/I5862.

References

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