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2020 Load balancing under $d$-thinning
Ohad Noy Feldheim, Jiange Li
Electron. Commun. Probab. 25(none): 1-13 (2020). DOI: 10.1214/19-ECP282


In the classical balls-and-bins model, $m$ balls are allocated into $n$ bins one by one uniformly at random. In this note, we consider the $d$-thinning variant of this model, in which the process is regulated in an on-line fashion as follows. For each ball, after a random bin has been selected, an overseer may decide, based on all previous history, whether to accept this bin or not. However, one of every $d$ consecutive suggested bins must be accepted. The maximum load of this setting is the number of balls in the most loaded bin. We show that after $\Theta (n)$ balls have been allocated, the least maximum load achievable with high probability is $(d+o(1))\sqrt [d]{\frac{d\log n} {\log \log n}}$. This should be compared with the related $d$-choice setting, in which the optimal maximum load achievable with high probability is $\frac{\log \log n} {\log d}+O(1)$.


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Ohad Noy Feldheim. Jiange Li. "Load balancing under $d$-thinning." Electron. Commun. Probab. 25 1 - 13, 2020.


Received: 27 August 2019; Accepted: 9 December 2019; Published: 2020
First available in Project Euclid: 3 January 2020

zbMATH: 1428.60102
MathSciNet: MR4053904
Digital Object Identifier: 10.1214/19-ECP282

Primary: 60J10, 68Q87


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