Issue RAIRO-Oper. Res. Volume 42, Number 4, October-December 2008 ALIO/EURO V Conference on Combinatorial Optimization Page(s) 455 - 467 DOI 10.1051/ro:2008028 Published online 04 April 2009

RAIRO-Oper. Res. 42 (2008) 455-467
DOI: 10.1051/ro:2008028

Acyclic Orientations with Path Constraints

Rosa M. V. Figueiredo¹, Valmir C. Barbosa², Nelson Maculan² and Cid C. de Souza<sup>3

1</sup>  Universidade do Estado do Rio de Janeiro, Instituto de Matemática e Estatística, 20550-900 Rio de Janeiro - RJ, Brazil; rosa@ime.uerj.br
²  Universidade Federal do Rio de Janeiro, Programa de Engenharia de Sistemas e Computação, COPPE, Caixa Postal 68511, 21941-972 Rio de Janeiro - RJ, Brazil; valmir@cos.ufrj.br maculan@cos.ufrj.br
³  Universidade Estadual de Campinas, Instituto de Computação, Caixa Postal 6176, 13084-971 Campinas - SP, Brazil; cid@ic.unicamp.br

Received May 11, 2005. Accepted January 9, 2008. Published online 4 April 2009

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.

Mathematics Subject Classification. 90C27, 90C57.

Key words: Acyclic orientations, path constraints, combinatorial optimization problems, facets of polyhedra.


© EDP Sciences, ROADEF, SMAI 2008

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