License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.61
URN: urn:nbn:de:0030-drops-173466
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17346/
Kim, Sung-Hwan ;
Cho, Hwan-Gue
Simple Order-Isomorphic Matching Index with Expected Compact Space
Abstract
In this paper, we present a novel indexing method for the order-isomorphic pattern matching problem (also known as order-preserving pattern matching, or consecutive permutation matching), in which two equal-length strings are defined to match when X[i] < X[j] iff Y[i] < Y[j] for 0 ≤ i,j < |X|. We observe an interesting relation between the order-isomorphic matching and the insertion process of a binary search tree, based on which we propose a data structure which not only has a concise structure comprised of only two wavelet trees but also provides a surprisingly simple searching algorithm. In the average case analysis, the proposed method requires ?(R(T)) bits, and it is capable of answering a count query in ?(R(P)) time, and reporting an occurrence in ?(lg |T|) time, where T and P are the text and the pattern string, respectively; for a string X, R(X) is the total time taken for the construction of the binary search tree by successively inserting the keys X[|X|-1],⋯,X[0] at the root, and its expected value is ?(|X|lgσ) where σ is the alphabet size. Furthermore, the proposed method can be viewed as a generalization of some other methods including several heuristics and restricted versions described in previous studies in the literature.
BibTeX - Entry
@InProceedings{kim_et_al:LIPIcs.ISAAC.2022.61,
author = {Kim, Sung-Hwan and Cho, Hwan-Gue},
title = {{Simple Order-Isomorphic Matching Index with Expected Compact Space}},
booktitle = {33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
pages = {61:1--61:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-258-7},
ISSN = {1868-8969},
year = {2022},
volume = {248},
editor = {Bae, Sang Won and Park, Heejin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17346},
URN = {urn:nbn:de:0030-drops-173466},
doi = {10.4230/LIPIcs.ISAAC.2022.61},
annote = {Keywords: Compact Data Structure, String Matching, Order-Preserving Matching, Suffix Array, FM-index, Binary Search Tree}
}
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Keywords: |
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Compact Data Structure, String Matching, Order-Preserving Matching, Suffix Array, FM-index, Binary Search Tree |
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Collection: |
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33rd International Symposium on Algorithms and Computation (ISAAC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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14.12.2022 |
