Distributed Gateway Placement for Cost Minimization in Wireless Mesh Networks

We study the problem of gateway placement for cost minimization (GPCM) in two-dimensional wireless mesh networks. We are given a set of mesh routers, assume they have identical transmission range r, represented by unit transmission disks around them. A router may be selected as a gateway at certain placing cost. A router is served by a gateway if and only if the gateway is within its transmission range. The goal of this work is to select a set of mesh routers as gateways to serve the rest routers with minimum overall cost. This problem is NP-hard. To the best of our knowledge, no distributed algorithm with a constant approximation ratio has been given before. When all weights are uniform, the best approximation ratio is 38. We present both centralized and distributed algorithms which can achieve approximation ratios 6 + ϵ and 20 respectively. Our algorithms greatly improve the best approximation ratios.