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arXiv · 1310.5367

Balanced Allocations: A Simple Proof for the Heavily Loaded Case

Kunal Talwar·Udi Wieder
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Abstract

We provide a relatively simple proof that the expected gap between the maximum load and the average load in the two choice process is bounded by $(1+o(1))\log \log n$, irrespective of the number of balls thrown. The theorem was first proven by Berenbrink et al. Their proof uses heavy machinery from Markov-Chain theory and some of the calculations are done using computers. In this manuscript we provide a significantly simpler proof that is not aided by computers and is self contained. The simplification comes at a cost of weaker bounds on the low order terms and a weaker tail bound for the probability of deviating from the expectation.

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Kunal Talwar, Udi Wieder. 2013-10-20. Balanced Allocations: A Simple Proof for the Heavily Loaded Case. https://arxiv.org/abs/1310.5367

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