# Acyclic Orientations with Path Constraints

Rosa M. V. Figueiredo; Valmir C. Barbosa; Nelson Maculan; Cid C. de Souza

RAIRO - Operations Research (2009)

- Volume: 42, Issue: 4, page 455-467
- ISSN: 0399-0559

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topFigueiredo, Rosa M. V., et al. "Acyclic Orientations with Path Constraints." RAIRO - Operations Research 42.4 (2009): 455-467. <http://eudml.org/doc/105414>.

@article{Figueiredo2009,

abstract = {
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.
},

author = {Figueiredo, Rosa M. V., Barbosa, Valmir C., Maculan, Nelson, de Souza, Cid C.},

journal = {RAIRO - Operations Research},

keywords = {Acyclic orientations; path constraints; combinatorial optimization problems; facets of polyhedra.; acyclic orientations; facets of polyhedra},

language = {eng},

month = {4},

number = {4},

pages = {455-467},

publisher = {EDP Sciences},

title = {Acyclic Orientations with Path Constraints},

url = {http://eudml.org/doc/105414},

volume = {42},

year = {2009},

}

TY - JOUR

AU - Figueiredo, Rosa M. V.

AU - Barbosa, Valmir C.

AU - Maculan, Nelson

AU - de Souza, Cid C.

TI - Acyclic Orientations with Path Constraints

JO - RAIRO - Operations Research

DA - 2009/4//

PB - EDP Sciences

VL - 42

IS - 4

SP - 455

EP - 467

AB -
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.

LA - eng

KW - Acyclic orientations; path constraints; combinatorial optimization problems; facets of polyhedra.; acyclic orientations; facets of polyhedra

UR - http://eudml.org/doc/105414

ER -

## References

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- R. Borndörfer, A. Eisenblätter, M. Grötschel, and A. Martin, The orientation model for frequency assignment problems. Technical Report 98-01, Zuse Institute Berlin, Germany (1998). Zbl0895.90090
- R.W. Deming, Acyclic orientations of a graph and chromatic and independence numbers. J. Combin. Theory Ser. B26 (1979) 101–110. Zbl0331.05110
- T. Gallai, On directed paths and circuits, in Theory of Graphs edited by P. Erdős and G. Katona, Academic Press, New York, NY (1968) 115–118.
- M. Grötschel, M. Jünger, and G. Reinelt, Facets of the linear ordering polytope. Math. Program.33 (1985) 43–60. Zbl0577.05035
- M. Grötschel, M. Jünger, and G. Reinelt, On the acyclic subgraph polytope. Math. Program.33 (1985) 28–42. Zbl0577.05034
- V. Maniezzo and A. Carbonaro, An ants heuristic for the frequency assignment problem. Future Gener. Comput. Syst.16 (2000) 927–935.
- B. Roy, Nombre chromatique et plus longs chemins d'un graphe, Revue AFIRO1 (1967) 127–132. Zbl0157.31302

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