We consider the problem of broadcasting in an unknown radio network modeled as a directed graph $G=(V,E)$, where $|V|=n$. In unknown networks, every node knows only its own label, while it is unaware of any other parameter of the network, including its neighborhood and even any upper bound on the number of nodes. We show an $\mathcal{O}(n\log n\log\log n)$ upper bound on the time complexity of deterministic broadcasting. This is an improvement over the currently best upper bound $\mathcal{O}(n\log^2n)$ for arbitrary networks, thus shrinking exponentially the existing gap between the lower bound $\Omega(n\log n)$ and the upper bound from $\mathcal{O}(\log n)$ to $\mathcal{O}(\log\log n)$.

A classical problem in addressing a decentralized multiple-access channel is resolving conflicts when a set of stations attempt to transmit at the same time on a shared communication channel. In a static scenario, i.e., when all stations are activated simultaneously, Komlós and Greenberg [IEEE Trans. Inform. Theory, 31 (1985), pp. 302--306] in their seminal work showed that it is possible to resolve the conflict among $k$ stations from an ensemble of $n$, with a nonadaptive deterministic algorithm in time $O(k + k \log(n/k))$ in the worst case. In this paper we show that in a dynamic scenario, when the stations can join the channel at arbitrary rounds, there is a nonadaptive deterministic algorithm guaranteeing a successful transmission for each station in only a slightly bigger time: $O(k\log n\log\log n)$ in the worst case. This almost matches the $\Omega(k\log n/\log k)$ lower bound by Greenberg and Winograd [J. ACM, 32 (1985), pp. 589--596] that holds even in much stronger settings: for adaptive algor...