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arXiv · 1303.4376

2-stack pushall sortable permutations

Adeline Pierrot·Dominique Rossin
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Abstract

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.

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Adeline Pierrot, Dominique Rossin. 2013-03-18. 2-stack pushall sortable permutations. https://arxiv.org/abs/1303.4376

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