The power of thinning in balanced allocation

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

Original languageAmerican English
Article number34
JournalElectronic Communications in Probability
Volume26
DOIs
StatePublished - 2021

Bibliographical note

Funding Information:
*Research was supported by the Israel Science Foundation (grant No. 1707/16). †Hebrew University of Jerusalem, Israel. E-mail: Ohad.Feldheim@mail.huji.ac.il ‡Hebrew University of Jerusalem, Israel. E-mail: Ori.Gurel-Gurevich@mail.huji.ac.il

Publisher Copyright:
© 2021, Institute of Mathematical Statistics. All rights reserved.

Keywords

  • (1 + α)-choice
  • Balanced allocation
  • Load balancing, balls and bins
  • One-retry
  • Subsampling
  • Thinning
  • Two-choices

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