Brute-Force Integer Max Flow Algorithm for Networks Under Reachability Restrictions

An exact algorithm for solving integer maximum flow problem under reachability restrictions is proposed. A computational complexity of brute-force method was obtained. Presented examples show main issues arising while solving network flow problems under reachability restrictions. Enhancements for reducing operations number and redundant computations are provided. Tree-structured networks are considered with respect to reachability restrictions. It is shown that the maximum flow problem can be solved in polynomial time for these networks.