The power of thinning in balanced allocation

TL;DR

This paper investigates a balanced allocation process where an overseer can choose to reallocate balls to minimize maximum load, presenting an asymptotically optimal strategy that achieves a near-optimal maximum load bound.

Contribution

It introduces a novel allocation strategy leveraging thinning to significantly reduce maximum load in balanced bin allocation.

Findings

Achieves maximum load of (1+o(1))√(8 log n / log log n)

Provides an asymptotically optimal strategy for load balancing

Demonstrates the power of thinning in allocation processes

Abstract

Balls are sequentially allocated into $n$ bins as follows: for each ball, an independent, uniformly random bin is generated. An overseer may then choose to either allocate the ball to this bin, or else the ball is allocated to a new independent uniformly random bin. The goal of the overseer is to reduce the load of the most heavily loaded bin after $\Theta(n)$ balls have been allocated. We provide an asymptotically optimal strategy yielding a maximum load of $(1+o(1))\sqrt{\frac{8\log n}{\log\log n}}$ balls.