Differential approximation results for the traveling salesman problem with distances 1 and 2

Jérôme Monnot (1) , Vangelis Paschos (1) , Sophie Toulouse (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We prove that both maximum and minimum traveling salesman problems on complete graphs with edge-distance 1 and 2 (denoted by min_TSP12 and max_TSP12, respectively) are approximable within 3/4. Based upon this result, we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3/4 to 7/8. Finally, we prove that, for any e>0, it is NP-hard to approximate both problems better than within 741/742 + e. The same resuts hold when dealing with a generalization of min_ and max_TSP, where instead of 1 and 2, edges are valued by a and b.

Mots clés: Differential ratio; Polynomial approximation; traveling salesman problem; Worst case analysis

Domaines: Algorithme et structure de données [cs.DS]; Optimisation et contrôle [math.OC]; Complexité [cs.CC]; Mathématique discrète [cs.DM]

Jérôme Monnot, Vangelis Paschos, Sophie Toulouse. Differential approximation results for the traveling salesman problem with distances 1 and 2. European Journal of Operational Research, 2003, 145(3), pp.537-548. ⟨hal-00003928⟩