An extended abstract of this work appeared at the 14th International Workshop on Randomization and Computation (RANDOM '10), p. 560–573.
Article first published online: 28 MAY 2012
Copyright © 2012 Wiley Periodicals, Inc.
Random Structures & Algorithms
Volume 43, Issue 2, pages 201–220, September 2013
How to Cite
Fountoulakis, N. and Panagiotou, K. (2013), Rumor spreading on random regular graphs and expanders. Random Struct. Alg., 43: 201–220. doi: 10.1002/rsa.20432
Parts of this work were performed while both authors were affiliated with the Max Planck Institute for Informatics, 66123 Saarbrücken, Germany.
- Issue published online: 24 JUL 2013
- Article first published online: 28 MAY 2012
- Manuscript Accepted: 16 JAN 2012
- Manuscript Received: 17 FEB 2010
- rumor spreading;
- random regular graphs;
- pseudorandom graphs;
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
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 . © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013