An efficiently solvable case of the minimum weight equivalent subgraph problem

Given a directed graph G(,), the problem of finding a minimum cardinality subset υ ⊆ such that the subgraph, G(,), preserves the reachability properties of G(,) is well known to be difficult. In this article, we consider a generalization which seeks a minimum weight subset υ satisfying the stated conditions where the weights of arcs in are assigned arbitrary integer values. A polynomial-time algorithm is given for the case where the underlying, undirected graph is series-parallel. Naturally, the stated algorithm subsumes the cardinality case on such graphs as well.