Actas de congresos
Acyclic Orientations With Path Constraints
Registro en:
Rairo - Operations Research. , v. 42, n. 4, p. 455 - 467, 2008.
3990559
10.1051/ro:2008028
2-s2.0-54249167489
Autor
Figueiredo R.M.V.
Barbosa V.C.
Maculan N.
De Souza C.C.
Institución
Resumen
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. © EDP Sciences. 42 4 455 467 Aardal, K., Hipolito, A., van Hoesel, C., Jansen, B., Roos, C., Terlaky, T., (1995) EUCLID CALMA radio link frequency assignment project: A branch-and-cut algorithm for the frequency assignment problem, , Technical report, Delft and Eindhoven Universities of Technology, The Netherlands Bermond, J., Bond, J., Martin, C., Pekec, A., Roberts, F., Optimal orientations of annular networks (2000) J. Interconnection Networks, 1, pp. 21-46 Bermond, J., Di Ianni, M., Flammini, M., Perennes, S., Acyclic orientations for deadlock prevention in interconnection networks (1997) Proceedings of the Workshop on Graph-Theoretic Concepts in Computer Science, pp. 52-64 Borndörfer, R., Eisenblätter, A., Grötschel, M., Martin, A., The orientation model for frequency assignment problems (1998), Technical Report 98-01, Zuse Institute Berlin, GermanyDeming, R.W., Acyclic orientations of a graph and chromatic and independence numbers (1979) J. Combin. Theory Ser. B, 26, pp. 101-110 Gallai, T., On directed paths and circuits (1968) Theory of Graphs, pp. 115-118. , edited by P. Erdös and G. Katona, Academic Press, New York, NY Grötschel, M., Jünger, M., Reinelt, G., Facets of the linear ordering polytope (1985) Math. Program, 33, pp. 43-60 Grötschel, M., Jünger, M., Reinelt, G., On the acyclic subgraph polytope (1985) Math. Program, 33, pp. 28-42 Maniezzo, V., Carbonaro, A., An ants heuristic for the frequency assignment problem (2000) Future Gener. Comput. Syst, 16, pp. 927-935 Roy, B., Nombre chromatique et plus longs chemins d'un graphe (1967) Revue AFIRO, 1, pp. 127-132