We study the problem of gossiping (all-to-all information exchange) in ad-hoc radio networks. Such a network is represented by a strongly-connected directed graph with $n$ vertices, whose topology is initially unknown to the protocol. In 2004, Gasieniec, Radzik, and Xin proposed a deterministic protocol with a running time of $\tilde{O}(n^{4/3})$, and closing the gap between their upper bound and the $\tilde{\Omega}(n)$ lower bound on the time complexity of gossiping remains a central open problem.
We develop a deterministic protocol for gossiping in ad-hoc radio networks that achieves a running time of $\tilde{O}((mn)^{3/5})$ for directed graphs with at most $m$ edges. Our protocol improves on the $\tilde{O}(n^{4/3})$ bound when $m = O(n^c)$ for $c < 1$.