We consider the vertex-weighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is series-parallel. For general graphs, this formulation can be interpreted as a (partial) extended formulation for the Steiner tree problem. By projecting this formulation, we obtain some very large classes of facet… CONTINUE READING

Network flow design III. Polyhedral characterization of the single source fixed costs problem on series-parallel graphs, " CORE Discussion Paper, Université

M. Schaffers

Catholique de Louvain ( Louvain-la-Neuve,

1991

A polynomial algorithm for the single source network flow design problem on series-parallel graphs, " CORE Discussion Paper 9062