Graphical balanced allocations and the (1 + β)-choice process

@article{Peres2015GraphicalBA,
  title={Graphical balanced allocations and the (1 + β)-choice process},
  author={Yuval Peres and Kunal Talwar and Udi Wieder},
  journal={Random Struct. Algorithms},
  year={2015},
  volume={47},
  pages={760-775}
}
Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well-known that the gap between the load of the most loaded bin and the average is ( √ m log n n ), for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to (log log n) independent of m. Consider a constrained setting where not all pairs of bins can be sampled. We are given a graph where each node corresponds to a bin. The process sequentially samples… CONTINUE READING

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