Document Open Access Logo

(Quantum) Complexity of Testing Signed Graph Clusterability

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

PDF
Thumbnail PDF

File

LIPIcs.TQC.2024.8.pdf
  • Filesize: 1.44 MB
  • 16 pages

Document Identifiers

Author Details

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

Cite As Get BibTex

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Florian Adriaens and Simon Apers. Testing cluster properties of signed graphs. In Proceedings of the ACM Web Conference 2023, pages 49-59, 2023. Google Scholar
  2. Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu. Estimating the distance to a monotone function. Random Structures & Algorithms, 31(3):371-383, 2007. Google Scholar
  3. Noga Alon. Testing subgraphs in large graphs. Random Structures & Algorithms, 21(3-4):359-370, 2002. Google Scholar
  4. Noga Alon, László Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of algorithms, 7(4):567-583, 1986. Google Scholar
  5. Noga Alon, Seannie Dar, Michal Parnas, and Dana Ron. Testing of clustering. SIAM Journal on Discrete Mathematics, 16(3):393-417, 2003. Google Scholar
  6. Noga Alon, Tali Kaufman, Michael Krivelevich, and Dana Ron. Testing triangle-freeness in general graphs. SIAM Journal on Discrete Mathematics, 22(2):786-819, 2008. Google Scholar
  7. Noga Alon and Michael Krivelevich. Testing k-colorability. SIAM Journal on Discrete Mathematics, 15(2):211-227, 2002. Google Scholar
  8. Noga Alon and Asaf Shapira. Testing satisfiability. Journal of Algorithms, 47(2):87-103, 2003. Google Scholar
  9. Noga Alon and Asaf Shapira. Every monotone graph property is testable. In Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, pages 128-137, 2005. Google Scholar
  10. Andris Ambainis, Aleksandrs Belovs, Oded Regev, and Ronald de Wolf. Efficient quantum algorithms for (gapped) group testing and junta testing. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 903-922. SIAM, 2016. Google Scholar
  11. Andris Ambainis, Andrew M Childs, and Yi-Kai Liu. Quantum property testing for bounded-degree graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pages 365-376. Springer, 2011. Google Scholar
  12. Simon Apers and Alain Sarlette. Quantum fast-forwarding: Markov chains and graph property testing. arXiv preprint, 2018. URL: https://arxiv.org/abs/1804.02321.
  13. Nikhil Bansal, Avrim Blum, and Shuchi Chawla. Correlation clustering. Machine learning, 56(1):89-113, 2004. Google Scholar
  14. Andrej Bogdanov, Kenji Obata, and Luca Trevisan. A lower bound for testing 3-colorability in bounded-degree graphs. In The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings., pages 93-102. IEEE, 2002. Google Scholar
  15. Sebastien Bubeck, Sitan Chen, and Jerry Li. Entanglement is necessary for optimal quantum property testing. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 692-703. IEEE, 2020. Google Scholar
  16. Harry Buhrman, Lance Fortnow, Ilan Newman, and Hein Röhrig. Quantum property testing. SIAM Journal on Computing, 37(5):1387-1400, 2008. Google Scholar
  17. Nilanjana Datta, Milan Mosonyi, Min-Hsiu Hsieh, and Fernando GSL Brandao. A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels. IEEE transactions on information theory, 59(12):8014-8026, 2013. Google Scholar
  18. James A Davis. Clustering and structural balance in graphs. Human relations, 20(2):181-187, 1967. Google Scholar
  19. Erik D Demaine, Dotan Emanuel, Amos Fiat, and Nicole Immorlica. Correlation clustering in general weighted graphs. Theoretical Computer Science, 361(2-3):172-187, 2006. Google Scholar
  20. Ilias Diakonikolas, Homin K Lee, Kevin Matulef, Krzysztof Onak, Ronitt Rubinfeld, Rocco A Servedio, and Andrew Wan. Testing for concise representations. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), pages 549-558. IEEE, 2007. Google Scholar
  21. Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes. Locally testable codes with constant rate, distance, and locality. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pages 357-374, 2022. Google Scholar
  22. Eldar Fischer, Guy Kindler, Dana Ron, Shmuel Safra, and Alex Samorodnitsky. Testing juntas. Journal of Computer and System Sciences, 68(4):753-787, 2004. Google Scholar
  23. Oded Goldreich. Short locally testable codes and proofs (survey). In Electronic Colloquium on Computational Complexity (ECCC), volume 14, 2005. Google Scholar
  24. Oded Goldreich. Property testing. Lecture Notes in Comput. Sci, 6390, 2010. Google Scholar
  25. Oded Goldreich, Shari Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. Journal of the ACM (JACM), 45(4):653-750, 1998. Google Scholar
  26. Oded Goldreich and Dana Ron. Property testing in bounded degree graphs. In Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pages 406-415, 1997. Google Scholar
  27. Tom Gur, Min-Hsiu Hsieh, and Sathyawageeswar Subramanian. Sublinear quantum algorithms for estimating von neumann entropy. arXiv preprint, 2021. URL: https://arxiv.org/abs/2111.11139.
  28. Frank Harary. On the notion of balance of a signed graph. Michigan Mathematical Journal, 2(2):143-146, 1953. Google Scholar
  29. Charanjit S Jutla, Anindya C Patthak, Atri Rudra, and David Zuckerman. Testing low-degree polynomials over prime fields. In 45th Annual IEEE Symposium on Foundations of Computer Science, pages 423-432. IEEE, 2004. Google Scholar
  30. Pieter W Kasteleyn. Dimer statistics and phase transitions. Journal of Mathematical Physics, 4(2):287-293, 1963. Google Scholar
  31. Tali Kaufman and Dana Ron. Testing polynomials over general fields. SIAM Journal on Computing, 36(3):779-802, 2006. Google Scholar
  32. Tali Kaufman and Madhu Sudan. Algebraic property testing: the role of invariance. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 403-412, 2008. Google Scholar
  33. Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Signed networks in social media. In Proceedings of the SIGCHI conference on human factors in computing systems, pages 1361-1370, 2010. Google Scholar
  34. Ting-Chun Lin and Min-Hsiu Hsieh. c 3-locally testable codes from lossless expanders. In 2022 IEEE International Symposium on Information Theory (ISIT), pages 1175-1180. IEEE, 2022. Google Scholar
  35. Ashley Montanaro and Ronald de Wolf. A survey of quantum property testing. arXiv preprint, 2013. URL: https://arxiv.org/abs/1310.2035.
  36. Roland Nagy, Matthias Widmann, Matthias Niethammer, Durga BR Dasari, Ilja Gerhardt, Öney O Soykal, Marina Radulaski, Takeshi Ohshima, Jelena Vučković, Nguyen Tien Son, et al. Quantum properties of dichroic silicon vacancies in silicon carbide. Physical Review Applied, 9(3):034022, 2018. Google Scholar
  37. Pavel Panteleev and Gleb Kalachev. Asymptotically good quantum and locally testable classical ldpc codes. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pages 375-388, 2022. Google Scholar
  38. Dana Ron et al. Property testing: A learning theory perspective. Foundations and Trendsregistered in Machine Learning, 1(3):307-402, 2008. Google Scholar
  39. Dana Ron et al. Algorithmic and analysis techniques in property testing. Foundations and Trendsregistered in Theoretical Computer Science, 5(2):73-205, 2010. Google Scholar
  40. Jiliang Tang, Yi Chang, Charu Aggarwal, and Huan Liu. A survey of signed network mining in social media. ACM Computing Surveys (CSUR), 49(3):1-37, 2016. Google Scholar
  41. Luca Trevisan. Some applications of coding theory in computational complexity. arXiv preprint, 2004. URL: https://arxiv.org/abs/cs/0409044.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact