Open Access
2021 The power of thinning in balanced allocation
Ohad N. Feldheim, Ori Gurel-Gurevich
Author Affiliations +
Electron. Commun. Probab. 26: 1-8 (2021). DOI: 10.1214/21-ECP400


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 Θ(n) balls have been allocated. We provide an asymptotically optimal strategy yielding a maximum load of (1+o(1))8lognloglogn balls.

Funding Statement

Research was supported by the Israel Science Foundation (grant No. 1707/16).


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Ohad N. Feldheim. Ori Gurel-Gurevich. "The power of thinning in balanced allocation." Electron. Commun. Probab. 26 1 - 8, 2021.


Received: 29 May 2020; Accepted: 6 May 2021; Published: 2021
First available in Project Euclid: 17 June 2021

Digital Object Identifier: 10.1214/21-ECP400

Primary: 60C05 , 68W27

Keywords: (1+α)-choice , balanced allocation , load balancing, balls and bins , one-retry , subsampling , thinning , two-choices

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