Transfinite Ford-Fulkerson on a finite network

It is well-known that the Ford-Fulkerson algorithm for finding a maximum flow in a network need not terminate if we allow the arc capacities to take irrational values. Every non-Terminating example converges to a limit flow, but this limit flow need not be a maximum flow. Hence, one may pass to the limit and begin the algorithm again. In this way, we may view the Ford-Fulkerson algorithm as a transfinite algorithm. We analyze the transfinite running-Time of the Ford-Fulkerson algorithm using ordinal numbers, and prove that the worst case running-Time is ω Θ (SCOPUS: ar.jinfo:eu-repo/semantics/publishe