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arXiv · 1012.5351

Quasirandom Rumor Spreading

Benjamin Doerr·Tobias Friedrich·Thomas Sauerwald
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Abstract

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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Benjamin Doerr, Tobias Friedrich, Thomas Sauerwald. 2010-12-24. Quasirandom Rumor Spreading. https://arxiv.org/abs/1012.5351

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