Simplicial homology based energy saving algorithms for wireless networks

Energy saving is one of the most investigated problems in wireless networks. In this paper, we introduce two homology based algorithms: a simulated annealing one and a robust one. These algorithms optimize the energy consumption at network level while maintaining the maximal coverage. By using simplicial homology, the complex geometrical calculation of the coverage is reduced to simple matrix computation. The simulated annealing algorithm gives a solution that approaches the global optimal one. The robust algorithm gives a local optimal solution. Our simulations show that this local optimal solution also approaches the global optimal one. Our algorithms can save at most 65% of system's maximal consumption power in polynomial time. The probability density function of the optimized radii of cells is also analyzed and discussed.