Simple Load Balancing
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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 ℓ_1 and ℓ_2 be their respective number of tokens. The two nodes exchange tokens such that they have (ℓ_1 + ℓ_2)/2 and (ℓ_1 + ℓ_2)/2 tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within O(nn + n Δ) steps, where Δ is the maximal initial load difference between any two nodes.
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