Neighbourhood Broadcasting in Hypercubes

Jean-Claude Bermond 1 Afonso Ferreira 1 Stéphane Pérennes 1 Joseph Peters 2
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : In the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least $\lceil \log_2 N \rceil$ rounds in a network of $N$ nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with $N$ nodes, each node has $\log_2 N$ neighbors, so neighborhood broadcasting takes at least $\lceil \log_2 \log_2 (N+1) \rceil$ rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes.
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Jean-Claude Bermond, Afonso Ferreira, Stéphane Pérennes, Joseph Peters. Neighbourhood Broadcasting in Hypercubes. Siam Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2007, 21 (4), pp.823-843. ⟨hal-00429191⟩

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