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Quantum Optimization
Quantum Simulation
Quantum Algorithm for Triangle Finding in Sparse Graphs
arXiv
Authors: François Le Gall, Shogo Nakajima
Year
2015
Paper ID
27958
Status
Preprint
Abstract Read
~2 min
Abstract Words
96
Citations
N/A
Abstract
This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent O\(n5/4\)-query algorithm given by Le Gall [FOCS 2014] for triangle finding over dense graphs (here n denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with O\(n5/4-ε\) queries for some constant ε>0 whenever the graph has at most O\(n2-c\) edges for some constant c>0.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al.
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