2026-08-17T09:43:32Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15693 2024-03-06T10:55:58Z ddc:004 open_access

Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems Le Gall, François Seddighin, Saeed Longest common substring Longest palindrome substring Quantum algorithms Sublinear algorithms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik François Le Gall and Saeed Seddighin 2022 Is Part Of LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2022.97 urn:nbn:de:0030-drops-156934 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.97 eng https://creativecommons.org/licenses/by/4.0/legalcode