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.2016.20
URN: urn:nbn:de:0030-drops-60744
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6074/
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Amit, Mika ; Bille, Philip ; Hagge Cording, Patrick ; Li Gørtz, Inge ; Wedel Vildhøj, Hjalte

Boxed Permutation Pattern Matching

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LIPIcs-CPM-2016-20.pdf (0.5 MB)

Abstract

Given permutations T and P of length n and m, respectively, the Permutation Pattern Matching problem asks to find all m-length subsequences of T that are order-isomorphic to P. This problem has a wide range of applications but is known to be NP-hard. In this paper, we study the special case, where the goal is to only find the boxed subsequences of T that are order-isomorphic to P. This problem was introduced by Bruner and Lackner who showed that it can be solved in O(n^3) time. Cho et al. [CPM 2015] gave an O(n^2m) time algorithm and improved it to O(n^2 log m). In this paper we present a solution that uses only O(n^2) time. In general, there are instances where the output size is Omega(n^2) and hence our bound is optimal. To achieve our results, we introduce several new ideas including a novel reduction to 2D offline dominance counting. Our algorithm is surprisingly simple and straightforward to implement.

BibTeX - Entry

@InProceedings{amit_et_al:LIPIcs:2016:6074,
  author =	{Mika Amit and Philip Bille and Patrick Hagge Cording and Inge Li G\ortz and Hjalte Wedel Vildh\oj},
  title =	{{Boxed Permutation Pattern Matching}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{20:1--20:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Roberto Grossi and Moshe Lewenstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6074},
  URN =		{urn:nbn:de:0030-drops-60744},
  doi =		{10.4230/LIPIcs.CPM.2016.20},
  annote =	{Keywords: Permutation, Subsequence, Pattern Matching, Order Preserving, Boxed Mesh Pattern}
}

Keywords: Permutation, Subsequence, Pattern Matching, Order Preserving, Boxed Mesh Pattern
Collection: 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)
Issue Date: 2016
Date of publication: 27.06.2016

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