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 : acyclic orientations, path constraints, combinatorial optimization problems, facets of polyhedra
@article{RO_2008__42_4_455_0,
author = {Rosa M. V. Figueiredo and Barbosa, Valmir C. and Maculan, Nelson and Cid C. de Souza},
title = {Acyclic orientations with path constraints},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {455--467},
publisher = {EDP-Sciences},
volume = {42},
number = {4},
year = {2008},
doi = {10.1051/ro:2008028},
mrnumber = {2469106},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2008028/}
}
TY - JOUR AU - Rosa M. V. Figueiredo AU - Barbosa, Valmir C. AU - Maculan, Nelson AU - Cid C. de Souza TI - Acyclic orientations with path constraints JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2008 SP - 455 EP - 467 VL - 42 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2008028/ DO - 10.1051/ro:2008028 LA - en ID - RO_2008__42_4_455_0 ER -
%0 Journal Article %A Rosa M. V. Figueiredo %A Barbosa, Valmir C. %A Maculan, Nelson %A Cid C. de Souza %T Acyclic orientations with path constraints %J RAIRO - Operations Research - Recherche Opérationnelle %D 2008 %P 455-467 %V 42 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro:2008028/ %R 10.1051/ro:2008028 %G en %F RO_2008__42_4_455_0
Rosa M. V. Figueiredo; Barbosa, Valmir C.; Maculan, Nelson; Cid C. de Souza. Acyclic orientations with path constraints. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 4, pp. 455-467. doi : 10.1051/ro:2008028. http://www.numdam.org/articles/10.1051/ro:2008028/
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