Deployment optimization of multi-hop wireless networks based on substitution graph

In multi-hop wireless networks, the maximum number of hops between clients and the service gateway (GW) significantly impacts the quality of network service, and thus GW deployment optimization plays a critical role in network design and planning. It is well know that the optimal GW deployment can be formulated as a vertex k-centre problem. However, achieving the optimal solution of a k-centre problem is highly complex due to its large solution space. To address this issue we propose a new algorithm based on the substitution principle of network by exploring the inclusion relationship of adjacent node subsets, to reduce the original network to a smaller scale substitution graph. The proposed algorithm can eliminate a large number of redundant nodes, thus reducing the solution space of the optimization problem, and improving the probability of achieving a globally optimal solution. The performance of the proposed algorithm is also analysed. Simulation results show that the proposed t-step substitution algorithm can significantly reduce the solution space of the k-centre problem by up to 80%. We then apply the proposed algorithms to traditional optimization methods, such as genetic (GA), artificial immune (AIA), and K-means for solving discrete space problems, and it is shown that the substitution based algorithm can significantly improve the performance of respective traditional GA, AIA and K-means methods,yielding a better GW deployment scheme with a smaller covering radius.