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Dynamic Averaging Load Balancing on Arbitrary Graphs

Authors Petra Berenbrink , Lukas Hintze, Hamed Hosseinpour , Dominik Kaaser , Malin Rau

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Author Details

Petra Berenbrink
  • Universität Hamburg, Germany
Lukas Hintze
  • Universität Hamburg, Germany
Hamed Hosseinpour
  • Universität Hamburg, Germany
Dominik Kaaser
  • TU Hamburg, Germany
Malin Rau
  • Universität Hamburg, Germany

Funding

  • Berenbrink, Petra: Supported by DFG Research Group ADYN (FOR 2975) under grant 411362735, and by DFG grant 427756233.
  • Hosseinpour, Hamed: Supported by DFG grant 427756233.
  • Rau, Malin: Supported by DFG Research Group ADYN (FOR 2975) under grant DFG 411362735.

Acknowledgements

We thank the anonymous reviewers for their comments.

Cite AsGet BibTex

Petra Berenbrink, Lukas Hintze, Hamed Hosseinpour, Dominik Kaaser, and Malin Rau. Dynamic Averaging Load Balancing on Arbitrary Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.18

Abstract

In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is averaged over the edges of that matching. We analyze the discrete case where load items are indivisible, moreover our results also carry over to the continuous case where load items can be split arbitrarily. For the choice of the matchings we consider three different models, random matchings of linear size, random matchings containing only single edges, and deterministic sequences of matchings covering the whole graph. We bound the discrepancy, which is defined as the difference between the maximum and the minimum load. Our results cover a broad range of graph classes and, to the best of our knowledge, our analysis is the first result for discrete and dynamic averaging load balancing processes. As our main technical contribution we develop a drift result that allows us to apply techniques based on the effective resistance in an electrical network to the setting of dynamic load balancing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Stochastic processes
  • Theory of computation → Distributed algorithms
Keywords
  • Dynamic Load Balancing
  • Distributed Computing
  • Randomized Algorithms
  • Drift Analysis

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