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arXiv · 1808.05389

Simple Load Balancing

Petra Berenbrink·Tom Friedetzky·Dominik Kaaser·Peter Kling
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Abstract

We consider the following load balancing process for $m$ tokens distributed arbitrarily among $n$ nodes connected by a complete graph: In each time step a pair of nodes is selected uniformly at random. Let $\ell_1$ and $\ell_2$ be their respective number of tokens. The two nodes exchange tokens such that they have $\lceil(\ell_1 + \ell_2)/2\rceil$ and $\lfloor(\ell_1 + \ell_2)/2\rfloor$ tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within $O(n\log{n} + n \log{\Delta})$ steps, where $\Delta$ is the maximal initial load difference between any two nodes.

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Petra Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling. 2018-08-16. Simple Load Balancing. https://arxiv.org/abs/1808.05389

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