  In this paper we improve the deterministic complexity of two fundamental
communication primitives in the classical model of ad-hoc radio networks with
unknown topology: broadcasting and wake-up. We consider an unknown radio
network, in which all nodes have no prior knowledge about network topology, and
know only the size of the network $n$, the maximum in-degree of any node
$\Delta$, and the eccentricity of the network $D$.
  For such networks, we first give an algorithm for wake-up, based on the
existence of small universal synchronizers. This algorithm runs in
$O(\frac{\min\{n, D \Delta\} \log n \log \Delta}{\log\log \Delta})$ time, the
fastest known in both directed and undirected networks, improving over the
previous best $O(n \log^2n)$-time result across all ranges of parameters, but
particularly when maximum in-degree is small.
  Next, we introduce a new combinatorial framework of block synchronizers and
prove the existence of such objects of low size. Using this framework, we
design a new deterministic algorithm for the fundamental problem of
broadcasting, running in $O(n \log D \log\log\frac{D \Delta}{n})$ time. This is
the fastest known algorithm for the problem in directed networks, improving
upon the $O(n \log n \log \log n)$-time algorithm of De Marco (2010) and the
$O(n \log^2 D)$-time algorithm due to Czumaj and Rytter (2003). It is also the
first to come within a log-logarithmic factor of the $\Omega(n \log D)$ lower
bound due to Clementi et al.\ (2003).
  Our results also have direct implications on the fastest \emph{deterministic
leader election} and \emph{clock synchronization} algorithms in both directed
and undirected radio networks, tasks which are commonly used as building blocks
for more complex procedures.
