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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{INTO_2022_208_a3,
     author = {I. M. Erusalimskyi and V. A. Skorokhodov and V. A. Rusakov},
     title = {Flows in networks with barrier reachability},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {24--28},
     publisher = {mathdoc},
     volume = {208},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_208_a3/}
}
TY  - JOUR
AU  - I. M. Erusalimskyi
AU  - V. A. Skorokhodov
AU  - V. A. Rusakov
TI  - Flows in networks with barrier reachability
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 24
EP  - 28
VL  - 208
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_208_a3/
LA  - ru
ID  - INTO_2022_208_a3
ER  - 
%0 Journal Article
%A I. M. Erusalimskyi
%A V. A. Skorokhodov
%A V. A. Rusakov
%T Flows in networks with barrier reachability
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 24-28
%V 208
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_208_a3/
%G ru
%F INTO_2022_208_a3
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/