(Non) -Approximability for the multi-criteria TSP (1,2)

E. Angel (1) , E. Bampis (1) , Laurent Gourvès (2) , Jérôme Monnot (2)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The approximability of multi-criteria combinatorial problems motivated a lot of articles. However, the non-approximability of this problems has never been investigated up to our knowledge. We propose a way to get some results of this kind which works for several problems and we put it into practice on a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1, 2)). Following the article of Angel et al. [1] who presented an approximation algorithm for the bi-criteria TSP(1, 2), we extend and improve the result to any number k of criteria.

Mots clés: non-approximability in multi-criteria optimization; design and analysis of algorithms

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

E. Angel, E. Bampis, Laurent Gourvès, Jérôme Monnot. (Non) -Approximability for the multi-criteria TSP (1,2). 2006. ⟨hal-00115511⟩