谣言的传播与行为

Flavio Chierichetti, George Giakkoupis, Silvio Lattanzi, A. Panconesi
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引用次数: 20

摘要

在本文中,我们研究了推拉式谣言传播的完成时间,也称为随机广播。我们证明了如果一个网络有n个节点,电导φ,那么推拉很有可能在O(log n/φ)多次通信回合内将消息传递给图中的所有节点。这个边界是最好的。在图稀疏化的基础上,给出了推拉完成时间被log n/φ多项式限定的另一种证明。虽然所得的渐近界不是最优的,但这个证明在谣言传播和图稀疏化之间显示了一个有趣的、意想不到的联系。最后,我们证明了如果网络中每条边的两个端点的度数相差不超过一个常数因子,那么单独PUSH和PULL都有高概率达到最优完成时间O(log n/φ)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rumor Spreading and Conductance
In this article, we study the completion time of the PUSH-PULL variant of rumor spreading, also known as randomized broadcast. We show that if a network has n nodes and conductance φ then, with high probability, PUSH-PULL will deliver the message to all nodes in the graph within O(log n/φ) many communication rounds. This bound is best possible. We also give an alternative proof that the completion time of PUSH-PULL is bounded by a polynomial in log n/φ, based on graph sparsification. Although the resulting asymptotic bound is not optimal, this proof shows an interesting and, at the outset, unexpected connection between rumor spreading and graph sparsification. Finally, we show that if the degrees of the two endpoints of each edge in the network differ by at most a constant factor, then both PUSH and PULL alone attain the optimal completion time of O(log n/φ), with high probability.
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