Introducing mass balancing theorem for network flow maximization

Maximization of flow through the network is required in many practical applications such as water supply flow networks, Oil and Gas flow networks, and transportation networks etc. In this paper a new theorem is presented that has direct application on maximization of flow through the network. This theorem suggests that the maximization of network flow can be achieved by visiting only unbalanced nodes rather than the whole network. Therefore based on this theorem a method is developed that maximizes flow thorough the network by visiting only unbalanced nodes. Hence this method can achieve solution in a sub-linear time where network has fewer unbalanced nodes. However this method has worst case complexity of order O(m2-m), where m is the number of edges. Furthermore it is shown that this theorem has also potential to make optimization an easier task in a multi-commodity flow environment.