Potential-Game Based Optimally Rigid Topology Control in Wireless Sensor Networks

In this paper, the optimally rigid topology control problem in wireless sensor networks is considered to improve the algebraic rigidity properties. This problem is first formulated as a constrained optimization problem which can be solved by two stages. A minimally rigid network is constructed in the first stage, then the optimally rigid topology in the second stage. A potential game approach is proposed for solving the optimization problem by choosing a different performance metric as the potential function. It can be seen that the proposed algorithm can significantly improve the network performance, such as reducing communication complexity and transmit power, prolonging network lifetime, and so on. Finally, some simulations demonstrate the effectiveness of the proposed algorithms from multiple perspectives: topology complexity, average degree, consensus convergence speed, average radius, average link length, and network lifetime.