Geodesic
Flows in networks with barrier reachability
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 24-28.

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The problem of flows in networks with barrier-type reachability restrictions is considered. We introduce new definitions that allow one to describe a flow in a network with reachability constraints, in particular, a representation of a flow as a vector-valued function. Conditions for preserving the flow and restricting the maximum flow along an arc are formulated in terms of vector-valued functions. This allows one to consider flow problems without passing to an unfolding, which is a graph with connected arcs.
Keywords: graph theory, nonstandard reachability, barrier reachability, network, flow in network, breakthrough algorithm. 
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I. M. Erusalimskyi; V. A. Skorokhodov; V. A. Rusakov. Flows in networks with barrier reachability. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 24-28. http://geodesic.mathdoc.fr/item/INTO_2022_208_a3/

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