Quantum Pattern Matching Fast on Average

The d -dimensional pattern matching problem is to find an occurrence of a pattern of length m × ⋯ × m within a text of length n × ⋯ × n , with n ≥ m . This task models various problems in text and image processing, among other application areas. This work describes a quantum algorithm which solves t...

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Vydáno v:Algorithmica Ročník 77; číslo 1; s. 16 - 39
Hlavní autor: Montanaro, Ashley
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2017
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Image processing
Mathematics of Computing
Pattern matching
Theory of Computation
Quantum algorithms
Average-case complexity
Pattern matching
Quantum query complexity
ISSN:0178-4617, 1432-0541
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Shrnutí:The d -dimensional pattern matching problem is to find an occurrence of a pattern of length m × ⋯ × m within a text of length n × ⋯ × n , with n ≥ m . This task models various problems in text and image processing, among other application areas. This work describes a quantum algorithm which solves the pattern matching problem for random patterns and texts in time O ~ ( ( n / m ) d / 2 2 O ( d 3 / 2 log m ) ) . For large m this is super-polynomially faster than the best possible classical algorithm, which requires time Ω ~ ( n d / 2 + ( n / m ) d ) . The algorithm is based on the use of a quantum subroutine for finding hidden shifts in d dimensions, which is a variant of algorithms proposed by Kuperberg.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-015-0060-4