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

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 resu...

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Veröffentlicht in:Algorithmica Jg. 85; H. 5; S. 1251 - 1286
Hauptverfasser: Le Gall, François, Seddighin, Saeed
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2023
Springer Nature B.V
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Lower bounds
Mathematics of Computing
Strings
Suffix trees
Theory of Computation
String algorithms
Quantum algorithms
Sublinear-time algorithms
Fine-grained complexity
ISSN:0178-4617, 1432-0541
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Zusammenfassung: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 O ~ ( n ) time algorithm for LPS, we prove that LCS needs at least time Ω ~ ( n 2 / 3 ) even for 0/1 strings.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-01066-z