In this paper we study two flow problems: the feasible flow problem in dynamic networks and the maximum flow problem in bipartite dynamic networks with lower bounds. We mention that the maximum flow problem in bipartite dynamic networks with lower bound was presented in paper [8] a . For these problems we give examples.
In this paper we study the maximum flow in bipartite dynamic network and make a synthesis of the papers [17], [18], [19], [20]. We solve this problem by dynamic approach and static approach. In a bipartite static network the several maximum algorithms can be substantially improved. The basic idea in these improvements is a two arcs push rule in case of maximum algorithms. For these problems we give examples.
An nontrivial extension of the maximal static flow problem is the maximal dynamic flow model, where the transit time to traverse an arc is taken into consideration. If the network parameters as capacities, arc traversal times, and so on, are constant over time, then a dynamic flow problem is said to be stationary. Research on flow in planar static network is motivated by the fact that more efficient algorithms can be developed by exploiting the planar structure of the graph. This article states and solves the maximum flow in directed (1, n) planar dynamic networks in the stationary case.
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