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.ITCS.2022.97
URN: urn:nbn:de:0030-drops-156934
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15693/
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Le Gall, François ; Seddighin, Saeed

Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems

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LIPIcs-ITCS-2022-97.pdf (0.7 MB)

Abstract

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms for these problems along with quantum lower bounds. Our results shed light on a very surprising fact: Although the classic solutions for LCS and LPS are almost identical (via suffix trees), their quantum computational complexities are different. While we give an exact Õ(√n) time algorithm for LPS, we prove that LCS needs at least time ̃ Ω(n^{2/3}) even for 0/1 strings.

BibTeX - Entry

@InProceedings{legall_et_al:LIPIcs.ITCS.2022.97,
  author =	{Le Gall, Fran\c{c}ois and Seddighin, Saeed},
  title =	{{Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{97:1--97:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15693},
  URN =		{urn:nbn:de:0030-drops-156934},
  doi =		{10.4230/LIPIcs.ITCS.2022.97},
  annote =	{Keywords: Longest common substring, Longest palindrome substring, Quantum algorithms, Sublinear algorithms}
}

Keywords: Longest common substring, Longest palindrome substring, Quantum algorithms, Sublinear algorithms
Collection: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue Date: 2022
Date of publication: 25.01.2022

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