M. Au-problème and . Sat, Il est également intéressant de souligner qu'on ne dispose pour le moment d'aucun résultat négatif, ni surtout d'aucun résultat négatif général Dans le domaine de l'approximation polynomiale, le théorème PCP a permis depuis 1990 d'obtenir de nombreux résultats négatifs, et continue d'être exploité dans ce cadre Dans le domaine des algorithmes exacts, on déduit de l'hypothèse ETH (qui affirme, informellement, qu'on ne peut résoudre aucun MAX k-SAT avec une complexité sous-exponentielle) des résultats négatifs pour bien des problèmes. Cependant, en approximation exponentielle, qui se situe au croisement de ces deux domaines, on ne dispose ni d'un tel théorème, ni d'une telle hypothèse (une hypothèse assez générale pour produire des résultats, tout en restant satisfaisante pour l'intuition). Les premiers pas commencent tout juste à être esquissés par des équipes. Il faudra sans doute à l'avenir commencer par produire des résultats négatifs pour des problèmes spécifiques. Il est probable que ce travail passe également par une caractérisation précise de réductions entre problèmes qui conservent les ratios d'approximation

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