Tight & Simple Load Balancing
Petra Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling · 2019
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 ℓ1and ℓ2be 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(n log n + n log Δ) steps with high probability, where Δ is the maximal initial load difference between any two nodes. This bound is asymptotically tight.