Latency-Efficient Distributed M2M Multicasting in Wireless Mesh Networks under Physical Interference Model

Wireless Mesh Network (WMN) is an emerging communication paradigm to enable resilient, cost-efficient and reliable services for the future-generation wireless networks. In this paper, we study the problem of multipoint-to-multipoint (M2M) multicasting in a WMN which aims to use the minimum number of time slots (minimum latency) to exchange messages among a group of $k$ mesh nodes in a WMN with $n$ mesh nodes under physical interference model. We study the M2M multicasting problem in a distributed environment where each participant only knows that there are $k$ participants and it does not know who are other $k-1$ participants among $n$ mesh nodes. It is well known that the computation of an optimal M2M multicasting schedule is {bfsl NP-hard}. We present a fully distributed deterministic algorithm for such an M2M multicasting problem and analyze its time complexity. We show that if the maximum hop distance between any two out of the $k$ participants is $d$, then the studied M2M multicasting problem can be solved in time $O(dlog n + k)$ with a polynomial-time computation in unit disk graphs, which is an almost optimal scheme in the sense that there exists a WMN topology, e.g., a line, in which the M2M multicasting cannot be completed in less than $Omega(d+k)$ units of time. From our best knowledge, it is the first time to investigate M2M multicasting problem in WMNs under physical interference model.