The data aggregation rate is presented to denote the compressing capability of a sensor node in the sensor
networks, and the distributed algorithm is proposed based on data aggregation to achieve an optimal routing scheme that
maximizes the network lifetime. The problem is formulated as a linear programming problem, and sub-gradient algorithm
is used to solve it in a distributed manner. The simulation results show that the proposed algorithm can reduce data traffic,
balance energy consumption, and prolong the network lifetime effectively.