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
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Charalampopoulos, Panagiotis ; Pissis, Solon P. ; Radoszewski, Jakub

Longest Palindromic Substring in Sublinear Time

LIPIcs-CPM-2022-20.pdf (0.8 MB)


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

  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 =		{},
  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: string algorithms, longest palindromic substring, longest common extension
Collection: 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)
Issue Date: 2022
Date of publication: 22.06.2022

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