Radio communication in random graphs: extended abstract
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Radio communication in random graphs
Journal of Computer and System Sciences - Special issue on network algorithms 2005
Agent-based randomized broadcasting in large networks
Discrete Applied Mathematics
On randomized broadcasting in star graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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Broadcasting process is to send a piece of information which resides at one nodein the graph to all the remaining nodes. At each time step, a node knows about the information can send it to one of its neighbors. The broadcast problem is to find the minimum time step needed. The problem is NP hard in general. For a random graph $G_{n,p}$, we are interested in at what value of $p$ there exists a broadcast tree of depth exactly $\lc \log _2n\rc $. Frieze and Molloy \cite{FriMo} show that $p$ is of magnitude $\Theta ( \ln n/n)$. In this paper, we give the exact threshold of theedge probability for the existence of such a tree.