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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| Vydáno v: | Algorithmica Ročník 85; číslo 5; s. 1251 - 1286 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Springer US
01.05.2023
Springer Nature B.V |
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| ISSN: | 0178-4617, 1432-0541 |
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| 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
O
~
(
n
)
time algorithm for LPS, we prove that LCS needs at least time
Ω
~
(
n
2
/
3
)
even for 0/1 strings. |
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| AbstractList | 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. Longest common substring (), longest palindrome substring (), and Ulam distance () 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 and are almost identical (via suffix trees), their quantum computational complexities are different. While we give an exact $${{\tilde{O}}}(\sqrt{n})$$ O ~ ( n ) time algorithm for , we prove that needs at least time $$\tilde{\Omega }(n^{2/3})$$ Ω ~ ( n 2 / 3 ) even for 0/1 strings. 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~(n2/3) even for 0/1 strings. |
| Author | Le Gall, François Seddighin, Saeed |
| Author_xml | – sequence: 1 givenname: François surname: Le Gall fullname: Le Gall, François email: legall@math.nagoya-u.ac.jp organization: Graduate School of Mathematics, Nagoya University – sequence: 2 givenname: Saeed surname: Seddighin fullname: Seddighin, Saeed organization: Toyota Technological Institute at Chicago |
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| Snippet | Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved... Longest common substring (), longest palindrome substring (), and Ulam distance () are three fundamental string problems that can be classically solved in near... |
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| SubjectTerms | 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 |
| Title | Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems |
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