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.CPM.2022.20
URN: urn:nbn:de:0030-drops-161472
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16147/
Charalampopoulos, Panagiotis ;
Pissis, Solon P. ;
Radoszewski, Jakub
Longest Palindromic Substring in Sublinear Time
Abstract
We revisit the classic algorithmic problem of computing a longest palidromic substring. This problem is solvable by a celebrated ?(n)-time algorithm [Manacher, J. ACM 1975], where n is the length of the input string. For small alphabets, ?(n) is not necessarily optimal in the word RAM model of computation: a string of length n over alphabet [0,σ) can be stored in ?(n log σ/log n) space and read in ?(n log σ/log n) time. We devise a simple ?(n log σ/log n)-time algorithm for computing a longest palindromic substring. In particular, our algorithm works in sublinear time if σ = 2^{o(log n)}. Our technique relies on periodicity and on the ?(n log σ/log n)-time constructible data structure of Kempa and Kociumaka [STOC 2019] that answers longest common extension queries in ?(1) time.
BibTeX - Entry
@InProceedings{charalampopoulos_et_al:LIPIcs.CPM.2022.20,
author = {Charalampopoulos, Panagiotis and Pissis, Solon P. and Radoszewski, Jakub},
title = {{Longest Palindromic Substring in Sublinear Time}},
booktitle = {33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
pages = {20:1--20:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-234-1},
ISSN = {1868-8969},
year = {2022},
volume = {223},
editor = {Bannai, Hideo and Holub, Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16147},
URN = {urn:nbn:de:0030-drops-161472},
doi = {10.4230/LIPIcs.CPM.2022.20},
annote = {Keywords: string algorithms, longest palindromic substring, longest common extension}
}
Keywords: |
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string algorithms, longest palindromic substring, longest common extension |
Collection: |
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33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022) |
Issue Date: |
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2022 |
Date of publication: |
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22.06.2022 |