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arXiv · 2311.10480

(Quantum) complexity of testing signed graph clusterability

Kuo-Chin Chen·Simon Apers·Min-Hsiu Hsieh
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Abstract

This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which yields a polynomial speedup over the best classical clusterability tester known [arXiv:2102.07587]. Second, we prove an $\tilde{\Omega}(\sqrt{N})$ classical query lower bound for testing clusterability, which nearly matches the upper bound from [arXiv:2102.07587]. This settles the classical query complexity of clusterability testing, and it shows that our quantum algorithm has an advantage over any classical algorithm.

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Kuo-Chin Chen, Simon Apers, Min-Hsiu Hsieh. 2023-11-17. (Quantum) complexity of testing signed graph clusterability. https://arxiv.org/abs/2311.10480

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