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

Eric Angel (1) , Evripidis Bampis (1) , Laurent Gourvès (1) , 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

Many papers deal with the approximability of multi-criteria optimization problems but only a small number of non-approximability results, which rely on NP-hardness, exist in the literature. In this paper, we provide a new way of proving non-approximability results which relies on the existence of a small size good approximating set (i.e. it holds even in the unlikely event of P=NP). This method may be used for several problems but here we illustrate it for a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1,2)). Following the article of Angel et al. (FCT 2003) who presented an approximation algorithm for the bi-criteria TSP(1,2), we extend and improve the result to any number k of criteria.

Domaines: Informatique; Recherche opérationnelle [math.OC]; Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Informatique et théorie des jeux [cs.GT]

Eric Angel, Evripidis Bampis, Laurent Gourvès, Jérôme Monnot. (Non)-approximability for the multi-criteria TSP(1,2). Proceedings of Fundamentals of Computation Theory (FCT 2005), 2005, Sweden. pp.329--340, ⟨10.1007/11537311_29⟩. ⟨hal-00341349⟩