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arXiv · 1501.04822

Self-Stabilizing Repeated Balls-into-Bins

Luca Becchetti·Andrea Clementi·Emanuele Natale·Francesco Pasquale·Gustavo Posta
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Abstract

We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration "legitimate" if its maximum load is $\mathcal{O}(\log n)$. We prove that, starting from any configuration, the process will converge to a legitimate configuration in linear time and then it will only take on legitimate configurations over a period of length bounded by any polynomial in $n$, with high probability (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins in $\mathcal{O}(n \log^2 n)$ rounds, w.h.p.

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Luca Becchetti, Andrea Clementi, Emanuele Natale, Francesco Pasquale, Gustavo Posta. 2015-01-20. Self-Stabilizing Repeated Balls-into-Bins. https://arxiv.org/abs/1501.04822

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