  In the study of radio networks, the tasks of broadcasting (propagating a
message throughout the network) and leader election (having the network agree
on a node to designate `leader') are two of the most fundamental global
problems, and have a long history of work devoted to them. This work has two
divergent strands: some works focus on exploiting the geometric properties of
wireless networks based in physical space, while others consider general
graphs. Algorithmic results in each of these avenues have often used quite
different techniques, and produced bounds using incomparable parametrizations.
  In this work, we unite the study of general-graph and geometric-based radio
networks, by adapting the broadcast and leader election algorithm of Czumaj and
Davies (JACM '21) to achieve a running-time parametrized by the independence
number of the network (i.e., the size of the maximum independent set). This
parametrization preserves the running time on general graphs, matching the best
known, but also improves running times to near-optimality across a wide range
of geometric-based graph classes.
  As part of this algorithm, we also provide the first algorithm for computing
a maximal independent set in general-graph radio networks. This algorithm runs
in $O(\log^3 n)$ time-steps, only a $\log n$ factor away from the
$\Omega(\log^2 n)$ lower bound.
