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 Õ (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.
Cite
CITATION STYLE
Le Gall, F., & Nakajima, S. (2015). Quantum Algorithm for Triangle Finding in Sparse Graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9472 LNCS, pp. 590–600). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-662-48971-0_50
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