This paper studies the data gathering problem in wireless networks, where data generated at the nodes has to be collected at a single sink. We investigate the relationship between routing optimality and fair resource management. In particular, we prove that for energy balanced data propagation, Pareto optimal routing and flow maximization are equivalent, and also prove that flow maximization is equivalent to maximizing the network lifetime. We algebraically characterize the network structures in which energy balanced data flows are maximal. Moreover, we algebraically characterize communication links which are not used by an optimal flow. This leads to the characterization of minimal network structures supporting the maximal flows.
We note that energy balance, although implying global optimality, is a local property that can be computed efficiently and in a distributed manner. We suggest online distributed algorithms for energy balance in different optimal network structures and numerically show their stability in particular setting. We remark that although the results obtained in this paper have a direct consequence in energy saving for wireless networks they do not limit themselves to this type of networks neither to energy as a resource. As a matter of fact, the results are much more general and can be used for any type of network and different type of resources.