A Gossiping Protocol for Sparse Ad-Hoc Radio Networks

2026-06-27

AI Summary

This work addresses the gossiping problem in sparse, self-organizing radio networks with unknown topology and proposes a deterministic distributed protocol. The protocol achieves a time complexity of $\widetilde{O}((mn)^{3/5})$ on directed graphs with $m$ edges and $\widetilde{O}(\Delta^{1/2}n)$ on $\Delta$-regular graphs. Notably, it is the first to break the classical $\widetilde{O}(n^{4/3})$ upper bound for sparse graphs where $m = O(n^c)$ with $c < 11/9$, thereby significantly approaching the $\widetilde{\Omega}(n)$ information-theoretic lower bound. By integrating graph-theoretic analysis with radio scheduling techniques, the proposed algorithm substantially outperforms existing gossiping protocols in low-density or regular network topologies.

Abstract

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 gave a \(\tilde O(n^{4/3})\)-time deterministic protocol for this problem, and closing the gap between their upper bound and the \(\tildeΩ(n)\) 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 running time \(\tilde O((mn)^{3/5})\) 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 \(c < 11/9\). We also present a \(\tilde O(Δ^{1/2} n)\)-time gossiping protocol for \(Δ\)-regular graphs.

Problem

• gossiping
• ad-hoc radio networks
• time complexity
• sparse networks
• all-to-all communication

Innovation

• gossiping protocol
• ad-hoc radio networks
• deterministic algorithm
• sparse graphs
• time complexity