Geodesic
Finding the k Most Vital Elements of an s-t Planar Directed Network
Yugoslav journal of operations research, Tome 10 (2000) no. 1, p. 13 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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For a given s-t planar directed network with lower and upper arc capacities we find those k arcs the removal of which minimizes the flow value of the maximum flow. Such arcs are called the k most vital arcs of the network. Analogously we find the k most vital nodes. Further more, we find the k bicriterial lexicographical most vital elements, the removal of which minimizes the maximum flow value first, and on the other hand, is the "cheapest" variant. Such problems arise if one wants to know in advance what the consequences will be if some of the network elements terminate their function or have to be switched off.
Classification : 90B10
Keywords: k most vital arcs/nodes, planarity of directed networks, multicriterial optimization on networks. 
@article{YJOR_2000_10_1_a1,
     author = {Dimiter Ivanchev},
     title = {Finding the k {Most} {Vital} {Elements} of an s-t {Planar} {Directed} {Network}},
     journal = {Yugoslav journal of operations research},
     pages = {13 },
     year = {2000},
     volume = {10},
     number = {1},
     zbl = {0997.90009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2000_10_1_a1/}
}
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Dimiter Ivanchev. Finding the k Most Vital Elements of an s-t Planar Directed Network. Yugoslav journal of operations research, Tome 10 (2000) no. 1, p. 13 . http://geodesic.mathdoc.fr/item/YJOR_2000_10_1_a1/