Quantum algorithms for finding constant-sized sub-hypergraphs

We develop a general framework to construct quantum algorithms that detect if a 3-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari a...

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Bibliographic Details
Published inTheoretical computer science Vol. 609; pp. 569 - 582
Main Authors Le Gall, François, Nishimura, Harumichi, Tani, Seiichiro
Format Journal Article
LanguageEnglish
Published Elsevier B.V 04.01.2016
Subjects
Algorithms
Associative
Complexity
Construction
Graphs
Hypergraphs
Methodology
Operators
Quantum algorithms
Quantum walk
Query processing
Hypergraphs
Quantum walk
Quantum algorithms
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Summary:We develop a general framework to construct quantum algorithms that detect if a 3-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari and Magniez (2013) [12], and extends the methodology designed by Lee, Magniez and Santha (2013) [18] for similar problems over graphs. As applications, we obtain a quantum algorithm for finding a 4-clique in a 3-uniform hypergraph on n vertices with query complexity O(n1.883), and a quantum algorithm for determining if a ternary operator over a set of size n is associative with query complexity O(n2.113).
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.10.006