At first discrete-differential processes are reduced to “shortest-path-problems” in graphs without approximation. For vector minimum problems, especially shortest-path-problems with vector-valued lengths of arcs, the notion of an optimal-efficient solution,. of an optimal-efficient path resp. with regard to a real-valued valuation is introduced. To compute an optimal-efficient path, analog of the algorithms of Bellman, Ford, Floyd and Dantzing for vector-valued lengths of arcs and generalized measures of paths are given.