Temporally repeated flow algorithms for dynamic min cost flows

Given a digraph G=(V, E), minimal cost network flow problems over T<∞ time periods are considered. The equivalence of this problem to a network flow problem in a digraph with nT nodes, the dynamic digraph GT, is reviewed. For large T, which often occurs in practical situations, this will make the complexity of min-cost flow algorithms intolerably large. The author proposes for problems with uniform input or output a solution procedure that deals with the original static digraph G. The main tools used in the procedure are the temporally repeated flow technique and the theory of lexicographical flows