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, which completes the task in $O(n \log D \log \log \frac{D \Delta}{n})$ time-steps, where $n$ is the number of nodes in the network, $\Delta$ is the maximum in-degree of any node, and $D$ is the eccentricity of the network. This comes within a log-logarithmic factor of the $\Omega(n \log D)$ lower bound due to Clementi et. al.