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DOI: 10.4230/LIPIcs.CPM.2016.20
URN: urn:nbn:de:0030-drops-60744
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6074/
Amit, Mika ; Bille, Philip ; Hagge Cording, Patrick ; Li Gørtz, Inge ; Wedel Vildhøj, Hjalte
Boxed Permutation Pattern Matching
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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 | |
| Seminar: | 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 27.06.2016 |
