  We study the single pair capacitated network design problem and the budget
constrained max flow problem on undirected series-parallel graphs. These
problems were well studied on directed series-parallel graphs, but little is
known in the context of undirected graphs. The major difference between the
cases is that the source and sink of the problem instance do not necessarily
coincide with the terminals of the underlying series-parallel graph in the
undirected case, thus creating certain complications. We provide
pseudopolynomial time algorithms to solve both of the problems and provide an
FPTAS for the budget constrained max flow problem. We also provide some
extensions, arguing important cases when the problems are polynomial-time
solvable, and describing a series-parallel gadget that captures an edge upgrade
version of the problems.
