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The Steiner tree problem. I: Formulations, compositions and extensions and extension of facets. (English) Zbl 0821.90124
Summary: We give some integer programming formulations for the Steiner tree problem on undirected and directed graphs and study the associated polyhedra. We give some families of facets for the undirected case along with some compositions and extensions. We also give a projection that relates the Steiner tree polyhedron on an undirected graph to the polyhedron for the corresponding directed graph. This is used to show that the LP-relaxation of the directed formulation is superior to the LP- relaxation of the undirected one.

90C35 Programming involving graphs or networks
90C10 Integer programming
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
Full Text: DOI
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