License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2018.14
URN: urn:nbn:de:0030-drops-86957
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8695/
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Zhang, Shu ; Zhu, Daming ; Jiang, Haitao ; Ma, Jingjing ; Guo, Jiong ; Feng, Haodi

Can a permutation be sorted by best short swaps?

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LIPIcs-CPM-2018-14.pdf (0.4 MB)

Abstract

A short swap switches two elements with at most one element caught between them. Sorting permutation by short swaps asks to find a shortest short swap sequence to transform a permutation into another. A short swap can eliminate at most three inversions. It is still open for whether a permutation can be sorted by short swaps each of which can eliminate three inversions. In this paper, we present a polynomial time algorithm to solve the problem, which can decide whether a permutation can be sorted by short swaps each of which can eliminate 3 inversions in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time, where n is the number of elements in the permutation.
A short swap can cause the total length of two element vectors to decrease by at most 4. We further propose an algorithm to recognize a permutation which can be sorted by short swaps each of which can cause the element vector length sum to decrease by 4 in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time. This improves upon the O(n^2) algorithm proposed by Heath and Vergara to decide whether a permutation is so called lucky.

BibTeX - Entry

@InProceedings{zhang_et_al:LIPIcs:2018:8695,
  author =	{Shu Zhang and Daming Zhu and Haitao Jiang and Jingjing Ma and Jiong Guo and Haodi Feng},
  title =	{{Can a permutation be sorted by best short swaps?}},
  booktitle =	{Annual Symposium on Combinatorial Pattern Matching  (CPM 2018)},
  pages =	{14:1--14:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Gonzalo Navarro and David Sankoff and Binhai Zhu},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2018/8695},
  URN =		{urn:nbn:de:0030-drops-86957},
  doi =		{10.4230/LIPIcs.CPM.2018.14},
  annote =	{Keywords: Algorithm, Complexity, Short Swap, Permutation, Reversal}
}

Keywords: Algorithm, Complexity, Short Swap, Permutation, Reversal
Collection: Annual Symposium on Combinatorial Pattern Matching (CPM 2018)
Issue Date: 2018
Date of publication: 18.05.2018

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