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In the study of radio networks, the tasks of broadcasting (propagating amessage throughout the network) and leader election (having the network agreeon a node to designate `leader') are two of the most fundamental globalproblems, and have a long history of work devoted to them. This work has twodivergent strands: some works focus on exploiting the geometric properties ofwireless networks based in physical space, while others consider generalgraphs. Algorithmic results in each of these avenues have often used quitedifferent techniques, and produced bounds using incomparable parametrizations.  In this work, we unite the study of general-graph and geometric-based radionetworks, by adapting the broadcast and leader election algorithm of Czumaj andDavies (JACM '21) to achieve a running-time parametrized by the independencenumber of the network (i.e., the size of the maximum independent set). Thisparametrization preserves the running time on general graphs, matching the bestknown, but also improves running times to near-optimality across a wide rangeof geometric-based graph classes.  As part of this algorithm, we also provide the first algorithm for computinga maximal independent set in general-graph radio networks. This algorithm runsin $O(\log^3 n)$ time-steps, only a $\log n$ factor away from the$\Omega(\log^2 n)$ lower bound.

Uniting General-Graph and Geometric-Based Radio Networks via Independence Number Parametrization