Abstract
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-defining valid inequalities for the Steiner tree polytope.
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Research supported by Air Force contract AFOSR-89-0271 and DARPA contract DARPA-89-5-1988.
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Goemans, M.X. The Steiner tree polytope and related polyhedra. Mathematical Programming 63, 157–182 (1994). https://doi.org/10.1007/BF01582064
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DOI: https://doi.org/10.1007/BF01582064