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Simple Load Balancing
Petra Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling
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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 ℓ₁ and ℓ₂ be their respective number of tokens. The two nodes exchange tokens such that they have ⌈(ℓ₁ + ℓ₂)/2⌉ and ⌊(ℓ₁ + ℓ₂)/2⌋ tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within O(nlogn + n logΔ) steps, where Δ is the maximal initial load difference between any two nodes.
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