Geodesic
Flows in generalized nets with related arcs
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 41-52

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The problem of finding the maximum flow in nets of a special form is considered. In such nets the arcs are related in such a way that the total flow passing through the related arcs does not exceed the minimum throughput of these arcs. It is shown that the theorem by Ford and Fulkerson, according to which the maximum flux value is equal to the throughput of a minimum cut, is not performed for such networks. The estimations of the maximum flow in a generalized net with bound arcs are proposed. And the algorithm for finding the maximum flow in such nets is developed.
Keywords: graph, graph algorithms, reachability, nonstandard reachability, flows on nets. 
@article{MAIS_2012_19_2_a2,
     author = {V. A. Skorokhodov},
     title = {Flows in generalized nets with related arcs},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {41--52},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a2/}
}
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V. A. Skorokhodov. Flows in generalized nets with related arcs. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 41-52. http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a2/