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(Quantum) Complexity of Testing Signed Graph Clusterability

Authors Kuo-Chin Chen , Simon Apers , Min-Hsiu Hsieh

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Kuo-Chin Chen
  • Hon Hai Research Institute, Taipei, Taiwan
Simon Apers
  • Université de Paris, CNRS, IRIF, France
Min-Hsiu Hsieh
  • Hon Hai Research Institute, Taipei, Taiwan

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Kuo-Chin Chen, Simon Apers, and Min-Hsiu Hsieh. (Quantum) Complexity of Testing Signed Graph Clusterability. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.TQC.2024.8

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 Õ(N^{1/3}) for testing clusterability, which yields a polynomial speedup over the best classical clusterability tester known [Adriaens and Apers, 2023]. Second, we prove an Ω̃(√N) classical query lower bound for testing clusterability, which nearly matches the upper bound from [Adriaens and Apers, 2023]. This settles the classical query complexity of clusterability testing, and it shows that our quantum algorithm has an advantage over any classical algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
  • Theory of computation → Graph algorithms analysis
Keywords
  • Quantum Algorithm
  • classical Query lower Bound
  • Graph Property testing

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