On the Steiner 2-edge connected subgraph polytope
Mahjoub, Ali Ridha; Pesneau, Pierre (2008), On the Steiner 2-edge connected subgraph polytope, RAIRO, 42, 3, p. 259-283. http://dx.doi.org/10.1051/ro:2008022
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Abstract (EN)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.
Subjects / KeywordsHalin graph; Steiner 2-edge connected graph; Polytope
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Pesneau, Pierre; Mahjoub, Ali Ridha; McCormick, S. Thomas; Fortz, bernard (2006) Article accepté pour publication ou publié