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DOI: 10.4230/LIPIcs.STACS.2014.614

2-Stack Sorting is polynomial

Authors: Adeline Pierrot and Dominique Rossin

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract

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.

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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)

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@InProceedings{pierrot_et_al:LIPIcs.STACS.2014.614,
  author =	{Pierrot, Adeline and Rossin, Dominique},
  title =	{{2-Stack Sorting is polynomial}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{614--626},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.614},
  URN =		{urn:nbn:de:0030-drops-44927},
  doi =		{10.4230/LIPIcs.STACS.2014.614},
  annote =	{Keywords: permutation, stack, sort, NP-complete}
}

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2-Stack Sorting is polynomial

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