平衡分配：重载情形的一个简单证明
Balanced Allocations: A Simple Proof for the Heavily Loaded Case
摘要：
我们提供了一个相对简单的证明，在两个选择过程中的最大负载和平均负载之间的预期差距是有界的$(1+o(1))\log \log n$，无论球的数量扔。这个定理首先由Berenbrink等人证明，他们的证明使用了马尔可夫链理论中的重型机器，一些计算是使用计算机完成的。在这份手稿中，我们提供了一个显着简单的证明，没有计算机的帮助，是自包含的。这种简化的代价是低阶项的边界较弱，偏离期望的概率的尾部边界较弱。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
