On flows in networks with reachability restrictions

Abstract

Abstract This paper we consider graphs with reachability restrictions of three types: barrier, valve and magnetic. As a part of the maximum flow problem in networks with considered restrictions, simple examples are given. These examples demonstrate a significant difference between flows in networks with reachability restrictions and flows in the same networks without any reachability restrictions. In each case under consideration there is a decrease of the maximum flow value. Wherein for magnetic reachability it is shown the possibility to control the network flow, whereas for barrier and valve reachability it is shown the reducing of the maximum flow due to the effect of superimposing of flow to itself, which is never observed in the classical theory of flows in networks.