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Rumor spreading on random regular graphs and expanders


  • An extended abstract of this work appeared at the 14th International Workshop on Randomization and Computation (RANDOM '10), p. 560–573.

  • Parts of this work were performed while both authors were affiliated with the Max Planck Institute for Informatics, 66123 Saarbrücken, Germany.


Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d -regular graphs with n vertices. We show that with probability 1 - o(1) the push model broadcasts the message to all nodes within (1 + o(1))Cd lnn rounds, where

equation image

Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo-random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 - o(1), where equation image. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013