Generalized Steiner problem in series-parallel networks
Journal of Algorithms
Minimum-weight two-connected spanning networks
Mathematical Programming: Series A and B
Integer polyhedra arising from certain network design problems with connectivity constraints
SIAM Journal on Discrete Mathematics
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
The Steiner tree polytope and related polyhedra
Mathematical Programming: Series A and B
Two-edge connected spanning subgraphs and polyhedra
Mathematical Programming: Series A and B
On two-connected subgraph polytopes
Discrete Mathematics
Steiner 2-Edge Connected Subgraph Polytopes on Series-Parallel Graphs
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
Let G=(V,E) be a undirected k-edge connected graph with weights c"e on edges and w"v on 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 we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. 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, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable.