Minimum cost flow algorithms for series-parallel networks

It is shown that an acyclic multigraph with a single source and a single sink is series-parallel if and only if for arbitrary linear cost functions and arbitrary capacities the corresponding minumum cost flow problem can be solved by a greedy algorithm. Furthermore, for networks of this type with m edges and n vertices, two O(mn+logm)-algorithms. One of them is based on the greedy scheme.