拟随机谣言传播
Quasirandom Rumor Spreading
摘要：
我们提出并分析了一个拟随机模拟的经典推送模型在网络中传播信息（“随机谣言传播”）。在经典模型中，在每一轮中，每个被通知的顶点随机选择一个邻居，如果它之前没有被通知，则通知它。这个简单的协议在完全图、超立方体、随机正则图、Erdos-Renyi随机图和Ramanujan图上以1-o（1）的概率在O（log n）轮内成功地将谣言从一个顶点传播到所有其他顶点。在拟随机模型中，我们假设每个顶点都有一个（循环的）邻居列表。一旦被通知，它就从列表上的随机位置开始，但从那时起，它就按照列表的顺序通知它的邻居。令人惊讶的是，无论列表的顺序如何，上述界限仍然成立。在某些情况下，甚至比经典模型更好的界限可以显示。
英文摘要：
We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, if it was not informed before. It is known that this simple protocol succeeds in spreading a rumor from one vertex to all others within O(log n) rounds on complete graphs, hypercubes, random regular graphs, Erdos-Renyi random graph and Ramanujan graphs with probability 1-o(1). In the quasirandom model, we assume that each vertex has a (cyclic) list of its neighbors. Once informed, it starts at a random position on the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above-mentioned bounds still hold. In some cases, even better bounds than for the classical model can be shown.
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