Latency-optimal communication in wireless mesh networks

Wireless mesh networking 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 Wireless Mesh Networks (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 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 O(D+ΔlognlogΔ) time units in any WMN of size n, diameter D  , and maximum degree Δ. This is an asymptotically optimal schedule in the sense that there exists a WMN topology, specifically a Δ-regular tree, in which the gossiping task cannot be accomplished in less than Ω(D+ΔlognlogΔ) units of time. Our algorithm also improves on currently best known gossiping schedule of length O(D+ΔlognlogΔ−loglogn) (Cicalese et al. (2009) [4]).