Computing the P 3 -hull number of a graph, a polyhedral approach
A subset S of vertices of a graph G=(V,E) is P 3 -convex if every simple path of three vertices starting and ending in S is contained in S. The P 3 -convex hull of S is the smallest P 3 -convex set containing S and the P 3 -hull number of G is the minimum number of vertices of a subset S such that i...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0166218X_v255_n_p155_Blaum |
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todo:paper_0166218X_v255_n_p155_Blaum2023-10-03T15:03:46Z Computing the P 3 -hull number of a graph, a polyhedral approach Blaum, M. Marenco, J. Combinatorial optimization Discrete convexity Facet-defining inequalities Hull number Combinatorial optimization Computational geometry Set theory Convex hull Convex set Discrete convexity Facet-defining inequalities Hull number NP-hard Polyhedral approach Polytopes Graph theory A subset S of vertices of a graph G=(V,E) is P 3 -convex if every simple path of three vertices starting and ending in S is contained in S. The P 3 -convex hull of S is the smallest P 3 -convex set containing S and the P 3 -hull number of G is the minimum number of vertices of a subset S such that its convex hull is V. It is a known fact that the calculation of the P 3 -hull number of a graph is NP-hard. In the present work we start the study of this problem from a polyhedral point of view, that is, we pose it as a binary IP problem and we study the associated polytope by exploring several families of facet-defining inequalities. © 2018 Elsevier B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0166218X_v255_n_p155_Blaum |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Combinatorial optimization Discrete convexity Facet-defining inequalities Hull number Combinatorial optimization Computational geometry Set theory Convex hull Convex set Discrete convexity Facet-defining inequalities Hull number NP-hard Polyhedral approach Polytopes Graph theory |
| spellingShingle |
Combinatorial optimization Discrete convexity Facet-defining inequalities Hull number Combinatorial optimization Computational geometry Set theory Convex hull Convex set Discrete convexity Facet-defining inequalities Hull number NP-hard Polyhedral approach Polytopes Graph theory Blaum, M. Marenco, J. Computing the P 3 -hull number of a graph, a polyhedral approach |
| topic_facet |
Combinatorial optimization Discrete convexity Facet-defining inequalities Hull number Combinatorial optimization Computational geometry Set theory Convex hull Convex set Discrete convexity Facet-defining inequalities Hull number NP-hard Polyhedral approach Polytopes Graph theory |
| description |
A subset S of vertices of a graph G=(V,E) is P 3 -convex if every simple path of three vertices starting and ending in S is contained in S. The P 3 -convex hull of S is the smallest P 3 -convex set containing S and the P 3 -hull number of G is the minimum number of vertices of a subset S such that its convex hull is V. It is a known fact that the calculation of the P 3 -hull number of a graph is NP-hard. In the present work we start the study of this problem from a polyhedral point of view, that is, we pose it as a binary IP problem and we study the associated polytope by exploring several families of facet-defining inequalities. © 2018 Elsevier B.V. |
| format |
JOUR |
| author |
Blaum, M. Marenco, J. |
| author_facet |
Blaum, M. Marenco, J. |
| author_sort |
Blaum, M. |
| title |
Computing the P 3 -hull number of a graph, a polyhedral approach |
| title_short |
Computing the P 3 -hull number of a graph, a polyhedral approach |
| title_full |
Computing the P 3 -hull number of a graph, a polyhedral approach |
| title_fullStr |
Computing the P 3 -hull number of a graph, a polyhedral approach |
| title_full_unstemmed |
Computing the P 3 -hull number of a graph, a polyhedral approach |
| title_sort |
computing the p 3 -hull number of a graph, a polyhedral approach |
| url |
http://hdl.handle.net/20.500.12110/paper_0166218X_v255_n_p155_Blaum |
| work_keys_str_mv |
AT blaumm computingthep3hullnumberofagraphapolyhedralapproach AT marencoj computingthep3hullnumberofagraphapolyhedralapproach |
| _version_ |
1807316068983635968 |