Single approximation for the biobjective Max TSP

Authors:
Cristina Bazgan;Laurent Gourvès;Jérôme Monnot;Fanny Pascual
Affiliations:
Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France and CNRS, UMR 7243, France and Institut Universitaire de France, France;CNRS, UMR 7243, France and Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;CNRS, UMR 7243, France and Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;Université Pierre et Marie Curie, LIP6, 4 place Jussieu, 75005 Paris, France
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

We mainly study the Max TSP with two objective functions. We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analyzed in three cases. When both (respectively, at least one) objective function(s) fulfill(s) the triangle inequality, the approximation ratio is 512-@e~0.41 (respectively, 38-@e). When the triangle inequality is not assumed on any objective function, the algorithm is 1+2214-@e~0.27-approximate.