Abstract
A mass balancing theorem (MBT) was recently introduced, concerning the role of 'unbalanced nodes' in the optimization of network flow. The MBT discovers and proves a flow-balancing property, which can be exploited in the design of network flow algorithms. Subsequently a number of such applications of the MBT have been explored for various types of flow-networks. These have included, in particular, single and multiple commodity networks with additional equipment of separators, which are present in various real world scenarios including the oil and gas industry. In this paper, the mass balancing theorem is revisited, and further developed to consider new network examples with embedded cycles. In doing so, algorithms based on the mass balancing method are extended to remove any undesirably saturated edges in the network, consequently reducing economic costs for flow-maximization in such networks.
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