Acyclic orientations with path constraints

Acyclic orientations with path constraints

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Article ID: iaor200944743
Country: France
Volume: 42
Issue: 4
Start Page Number: 455
End Page Number: 467
Publication Date: Oct 2008
Journal: RAIRO Operations Research
Authors: , , ,
Keywords: graphs, programming: linear
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.

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