Volume 42, Number 3, July-September 2008
|Page(s)||259 - 283|
|Published online||20 August 2008|
On the Steiner 2-edge connected subgraph polytope
LIMOS, CNRS, Univ. Blaise Pascal, Clermont Ferrand II,
Complexe Sci. des Cézeaux, 63177 Aubière Cedex; present address: LAMSADE, CNRS, Univ. Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775 Paris Cedex 16, France email@example.com
2 Université Bordeaux 1, IMB, 351, Cours de la Libération, 33 405 Talence Cedex, France; firstname.lastname@example.org
Accepted: 1 August 2007
In this paper, we study the Steiner 2-edge connected subgraph polytope. We introduce a large class of valid inequalities for this polytope called the generalized Steiner F-partition inequalities, that generalizes the so-called Steiner F-partition inequalities. We show that these inequalities together with the trivial and the Steiner cut inequalities completely describe the polytope on a class of graphs that generalizes the wheels. We also describe necessary conditions for these inequalities to be facet defining, and as a consequence, we obtain that the separation problem over the Steiner 2-edge connected subgraph polytope for that class of graphs can be solved in polynomial time. Moreover, we discuss that polytope in the graphs that decompose by 3-edge cutsets. And we show that the generalized Steiner F-partition inequalities together with the trivial and the Steiner cut inequalities suffice to describe the polytope in a class of graphs that generalizes the class of Halin graphs when the terminals have a particular disposition. This generalizes a result of Barahona and Mahjoub  for Halin graphs. This also yields a polynomial time cutting plane algorithm for the Steiner 2-edge connected subgraph problem in that class of graphs.
Mathematics Subject Classification: 05C85 / 90C27
Key words: Polytope / Steiner 2-edge connected graph / Halin graph.
© EDP Sciences, ROADEF, SMAI, 2008
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