# Networks and Distributed Systems

and F. Manne (2009)

# Latency-Optimal Communication in Wireless Mesh Networks

In: Proceedings of the 15th Asia-Pacific Conference on Communications (APCC 2009), ed. by " ", IEEE (ISBN: 978-1-4244-4784-8)

Wireless Mesh Networking (WMN) is an emerging communication paradigm to enable resilient, cost-efficient and reliable services for the future-generation wireless networks. We study the minimum-latency communication primitive of gossiping (all-to-all communication) in known topology WMNs, i.e., where the schedule of transmissions is pre-computed in advance based on full knowledge about the size and the topology of the Wireless Mesh Network (WMN). Each mesh node in the WMN is initially given a message and the objective is to design a minimum-latency schedule such that each mesh node distributes its message to all other mesh nodes. The problem of computing a minimum-latency gossiping schedule for a given WMN is NP-hard, hence it is only possible to get a polynomial approximation algorithm. In this paper, we show a deterministic approximation algorithm that can complete gossiping task in $(D+\frac{\Delta\log n}{\log{\Delta}})$ time units in any WMN of size $n,$ diameter $D$, and maximum degree $\Delta$. This is an asymptotically optimal schedule in the sense that there exists a WMN topology, specifically a $\Delta$-regular tree, in which the gossiping task cannot be accomplished in less than $\Omega(D+\frac{\Delta\log n}{\log{\Delta}})$ units of time. Our algorithm also improves on currently best known gossiping schedule of length $O(D+\frac{\Delta\log n}{\log{\Delta}-\log{\log n}})$ in [Algorithmica 54(2):226-242, 2009].