Some formulations for the group steiner tree problem

Authors:
Carlos E. Ferreira;Fernando M. de Oliveira Filho
Affiliations:
Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Brazil;Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Brazil
Venue:
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Year:
2006

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Abstract

The group Steiner tree problem consists of, given a graph G, a collection R of subsets of V(G) and a cost c(e) for each edge of G, finding a minimum-cost subtree that connects at least one vertex from each R ∈ R. It is a generalization of the well-known Steiner tree problem that arises naturally in the design of VLSI chips. In this paper, we study a polyhedron associated with this problem and some extended formulations. We give facet defining inequalities and explore the relationship between the group Steiner tree problem and other combinatorial optimization problems.