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- W4239759898 abstract "Dedicated to Manfred Padberg on the occasion of his 60th birthday.Given a graph G = (V, E) with edge weights and an integer vector r ∈ ℤ+v associated with the nodes of V, the survivable network design problem is to find a minimum weighted subgraph of G such that between every pair of nodes s, t of V there are at least min{r(s), r(t)} edge-disjoint paths. In this chapter we consider that problem when r ∈ {1, 2}V. This case is of particular interest to the telecommunication industry. We first consider the case when r(v) = 2 for all v ∈ V. We describe sufficient conditions for the so-called F-partition inequalities to define facets for the associated polytope. As a consequence, we show that the critical extreme points of the linear relaxation of that polytope may be separated in polynomial time using F-partition facets.Next we consider the case where r ∈ {1, 2}V. We first describe valid inequalities that generalize the F-partition inequalities. We discuss separation algorithms for these inequalities as well as for the so-called partition inequalities. Finally, we introduce a branch-and-cut algorithm based on these results and present some computational results. These show that the F-partition inequalities are very effective for the 2-connected subgraph problems." @default.
- W4239759898 created "2022-05-12" @default.
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- W4239759898 date "2004-01-01" @default.
- W4239759898 modified "2023-10-14" @default.
- W4239759898 title "9. (1, 2)-Survivable Networks: Facets and Branch-and-Cut" @default.
- W4239759898 doi "https://doi.org/10.1137/1.9780898718805.ch9" @default.
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