2-stack pushall sortable permutations

Adeline Pierrot (1) , Dominique Rossin (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

In the 60's, Knuth introduced stack-sorting and serial compositions of stacks. In particular, one significant question arise out of the work of Knuth: how to decide efficiently if a given permutation is sortable with 2 stacks in series? Whether this problem is polynomial or NP-complete is still unanswered yet. In this article we introduce 2-stack pushall permutations which form a subclass of 2-stack sortable permutations and show that these two classes are closely related. Moreover, we give an optimal O(n^2) algorithm to decide if a given permutation of size n is 2-stack pushall sortable and describe all its sortings. This result is a step to the solve the general $2$-stack sorting problem in polynomial time.

Mots clés: permutations; algorithm; sorting network; stack sorting

Domaines: Combinatoire [math.CO]

Adeline Pierrot, Dominique Rossin. 2-stack pushall sortable permutations. 2013. ⟨hal-00801861⟩