Resultats d’approximation polynomiale differentielle pour les versions minimisation et maximisation du probleme du voyageur du commerce

We prove that both minimum and maximum traveling salesman problems can be approximately solving, in polynomial time, by a constant-ratio differential approximation algorithm. Based upon this result, we then improve the standard approximation ratio known for maximum traveling salesman with distances 1 and

1. Finally, we prove that, for any $\epsilon > 0$, it is \textbf{NP}-hard to approximate both problems within better than $4707/4708 + \epsilon$.