2-Stack Sorting is polynomial

Authors Adeline Pierrot, Dominique Rossin

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Adeline Pierrot
Dominique Rossin

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Adeline Pierrot and Dominique Rossin. 2-Stack Sorting is polynomial. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 614-626, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


This article deals with deciding whether a permutation is sortable with two stacks in series. Whether this decision problem lies in P or is NP-complete is a longstanding open problem since the introduction of serial compositions of stacks by Knuth in The Art of Computer Programming in 1973. We hereby prove that this decision problem lies in P by giving a polynomial algorithm to solve it. This algorithm uses the concept of pushall sorting, which was previously defined and studied by the authors.
  • permutation
  • stack
  • sort
  • NP-complete


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