P. Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling
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引用次数: 12
摘要
我们考虑m个令牌随机分布在由完全图连接的n个节点上的负载平衡过程。在每个时间步长中均匀随机选择一对节点。设_1和_2是它们各自的符号数。这两个节点交换令牌，使它们分别具有< <(__1 + __2)/2²和< __1 + __2)/2²令牌。我们提供了一个简单的分析，表明该过程在O(n log n + n log Δ)步内以高概率达到几乎完美的平衡，其中Δ是任意两个节点之间的最大初始负载差。这个界是渐近紧的。
We consider the following load balancing process for m tokens distributed arbitrarily among n nodes connected by a complete graph. In each time step a pair of nodes is selected uniformly at random. Let ℓ_1 and ℓ_2 be their respective number of tokens. The two nodes exchange tokens such that they have ⌈(ℓ_1 + ℓ_2)/2⌉ and ⌈(ℓ_1 + ℓ_2)/2⌉ tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within O(n log n + n log Δ) steps with high probability, where Δ is the maximal initial load difference between any two nodes. This bound is asymptotically tight.
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