Optimal Association in Wireless Mesh Networks

The wireless multihop backhaul is a unique feature of wireless mesh networks (WMNs), which necessitates redesign of association control algorithms. In this paper, we formulate and propose approximation algorithms for the problem of optimal joint association and bandwidth allocation in WMNs, considering max-min fairness (MM) and proportional fairness (PF) objectives. We first relax the integral association constraint and get an optimal fractional association solution. Then, we propose two rounding algorithms, namely, largest fraction rounding and bipartite graph rounding, to get an integral solution and analyze their theoretical approximation ratios. Finally, we propose two approximation ratio improvement algorithms so that the improved approximation ratio can more accurately reflect the true performance gap between the produced solution and the optimal one. Our simulation results show that the proposed algorithms achieve performance that is close to the optimal and outperform popular heuristic algorithms. We also compare the performance of PF and MM in WMNs in terms of network throughput and fairness in user bandwidth. Finally, we compare the performances of the proposed rounding algorithms and show that the approximation ratio can be reduced to 1-2 by the proposed ratio improvement algorithms. Therefore, our proposed algorithm is able to achieve nearly optimal association control, as well as bandwidth allocation, considering MM or PF, with small approximation ratios, in WMNs.