Almost Optimal Deterministic Broadcast in Radio Networks

In this paper we present the fastest known algorithm for the fundamental problem of deterministic broadcast in ad-hoc radio networks with unknown topology. It completes the task inO(n logD log log D∆ n ) time-steps, where n is the number of nodes in the network, ∆ is the maximum in-degree of any node, and D is the eccentricity of the network. This improves upon the O(n log n log log n)-time algorithm of De Marco, and comes within a log-logarithmic factor of the Ω(n logD) lower bound due to Clementi et al.

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