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The node-edge weighted 2-edge connected subgraph problem : linear relaxation, facets and separation

Author

Listed:
  • Mourad Baïou

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • José Rafael Correa

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

Let G=(V,E) be an undirected 2-edge connected graph with weights on its edges and nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G , of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP is studied. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, a class of new valid inequalities is defined together with sufficient conditions for them to be facet-defining. Finally, a polynomial time algorithm is given to separate a subclass of these new iinequalities. As a consequence, all these new inequalities may be separated in polynomial time when G is series-parallel.

Suggested Citation

  • Mourad Baïou & José Rafael Correa, 2003. "The node-edge weighted 2-edge connected subgraph problem : linear relaxation, facets and separation," Working Papers hal-00242945, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242945
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242945
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