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arXiv · 1507.06878

Quantum Algorithm for Triangle Finding in Sparse Graphs

François Le Gall·Shogo Nakajima
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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 $\tilde O(n^{5/4})$-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 $O(n^{5/4-ε})$ queries for some constant $ε>0$ whenever the graph has at most $O(n^{2-c})$ edges for some constant $c>0$.

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François Le Gall, Shogo Nakajima. 2015-07-24. Quantum Algorithm for Triangle Finding in Sparse Graphs. https://doi.org/10.1007/s00453-016-0267-z

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