Optimize Wireless Networks for Energy Saving by Distributed Computation of Cech Complex

In this paper, we introduce a distributed algorithm to compute the. Cech complex. This algorithm is aimed at solving the coverage problems in self organized wireless networks. The complexity to compute the minimal Cech complex that gives information about coverage and connectivity of the network is O(n(2)), where n is the average number of neighbors of each cell. An application based on the distributed computation of the Cech complex, which is aimed at optimizing the wireless network for energy saving, is also proposed. This application also has polynomial complexity. The performance of the proposed algorithm and its application are evaluated. The simulation results show that the distributed computation of the Cech complex provides a consistent outcome with the one obtained by the centralized computation that is introduced in [6], while requires a much shorter calculation time. The optimized coverage saves 65% of the total transmission power, while also keeps the maximal coverage for the network.