Acyclic orientations with path constraints

Rosa Figueiredo (1) , Valmir C Barbosa (2) , Nelson Maculan (2) , Cid C de Souza (3)

1 LIA - Laboratoire Informatique d'Avignon
2 COPPE-UFRJ - Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia
3 UNICAMP - Universidade Estadual de Campinas = University of Campinas

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities.

Mots clés: facets of polyhedra; combinatorial optimization problems; Acyclic orientations; path constraints

Domaines: Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Rosa Figueiredo, Valmir C Barbosa, Nelson Maculan, Cid C de Souza. Acyclic orientations with path constraints. RAIRO - Operations Research, 2009, 42 (4), pp.455-467. ⟨10.1051/ro:2008028⟩. ⟨hal-02184964⟩