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.ISAAC.2017.35
URN: urn:nbn:de:0030-drops-82566
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8256/
Ganguly, Arnab ;
Shah, Rahul ;
Thankachan, Sharma V.
Structural Pattern Matching - Succinctly
Abstract
Let T be a text of length n containing characters from an alphabet \Sigma, which is the union of two disjoint sets: \Sigma_s containing static characters (s-characters) and \Sigma_p containing parameterized characters (p-characters).
Each character in \Sigma_p has an associated complementary character from \Sigma_p.
A pattern P (also over \Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y.
The task is to find the starting positions (occurrences) of all such substrings S.
Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires \Theta(n\log n) bits of space, and can find all occ occurrences in time O(|P|\log \sigma+ occ), where \sigma = |\Sigma|.
In this paper, we present the first succinct index for this problem, which occupies n \log \sigma + O(n) bits and offers O(|P|\log\sigma+ occ\cdot \log n \log\sigma) query time.
BibTeX - Entry
@InProceedings{ganguly_et_al:LIPIcs:2017:8256,
author = {Arnab Ganguly and Rahul Shah and Sharma V. Thankachan},
title = {{Structural Pattern Matching - Succinctly}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {35:1--35:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Yoshio Okamoto and Takeshi Tokuyama},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8256},
URN = {urn:nbn:de:0030-drops-82566},
doi = {10.4230/LIPIcs.ISAAC.2017.35},
annote = {Keywords: Parameterized Pattern Matching, Suffix tree, Burrows-Wheeler Transform, Wavelet Tree, Fully-functional succinct tree}
}
Keywords: |
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Parameterized Pattern Matching, Suffix tree, Burrows-Wheeler Transform, Wavelet Tree, Fully-functional succinct tree |
Collection: |
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28th International Symposium on Algorithms and Computation (ISAAC 2017) |
Issue Date: |
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2017 |
Date of publication: |
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07.12.2017 |