2-堆栈可排序排列
2-stack pushall sortable permutations
摘要：
在60年代，Knuth引入了堆栈排序和堆栈的串行组合。特别是，一个重要的问题产生的工作克努特：如何有效地决定，如果一个给定的排列是排序与2堆栈系列？这个问题是多项式问题还是NP-完全问题，目前还没有定论。在这篇文章中，我们介绍了2-栈pushall排列，形成了一个子类的2-栈可排序排列，并表明这两个类是密切相关的。此外，我们给出了一个O（n^2）的最优算法来决定一个给定的大小为n的置换是否是2-stack pushall可排序的，并描述了它的所有排序。这一结果为在多项式时间内解决一般的2-栈排序问题迈出了一步。
英文摘要：
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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