Minimum-Latency Gossiping in Multi-hop Wireless Mesh Networks

Wireless Mesh Networks (WMNs) 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 multi-hop ad-hoc WMNs. 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. Minimum-latency gossiping problem is known to be NP-hard even for the scenario in which the topology of the WMN is known to all mesh nodes in advance. We show an approximation scheme that can complete gossiping task in O(n log(3/2) n) time units with high probability at least 1 - 1/n in any ad-hoc WMN of size n. Our algorithm allows the labels (identifiers) of the mesh nodes to be polynomially large in n. To the best of our knowledge, this is the first time that randomized algorithm has been considered in ad-hoc WMNs with large labels. Moreover, our gossiping scheme also significantly improved all current gossiping algorithms in terms of approximation ratio. Our work has approximation ratio at most O(log(3/2) n) which is a great improvement of the current best known state-of-the-art algorithm with approximation ratio O(log(2) n) but for linearly large node labels by Czumaj and Rytter [11] [FOCS'03].