Steiner trees with n terminals among n + 1 nodes

Authors:
Alain Prodon
Affiliations:
Ecole Polytechnique Fédérale de Lausanne, Département de Mathématiques, MA - Ecublens, 1015 Lausanne, Switzerland
Venue:
Operations Research Letters
Year:
1992

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Abstract

Let G = (V, E) be a connected undirected graph and N a subset of distinguishednodes, called terminals. A Steiner tree on [G, N] is a minimal tree connecting all the terminal nodes. Restricting the instances to the case @?N@? = @?V@? -1, we present an algorithm to construct a minimum weight Steiner tree for any weight function on the edges E of G, and a complete minimal description of the polytope defined as the convex hull of all steiner trees on [G, N].