Document Open Access Logo

Query Lower Bounds for Correlation Clustering Under Memory Constraints

Authors Sumegha Garg , Songhua He , Periklis A. Papakonstantinou

PDF

File

Thumbnail PDF
PDF
LIPIcs.ITCS.2026.67.pdf
  • Filesize: 0.87 MB
  • 24 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Lower bounds and information complexity
Keywords
  • correlation clustering
  • query-space complexity
  • information theory

Metrics

Abstract

This work initiates the study of memory–query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non‑edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of ε n², any algorithm requires Ω(n/ε²) adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make ≫ n/ε² adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.

Cite As Get BibTex

Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou. Query Lower Bounds for Correlation Clustering Under Memory Constraints. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.67

Author Details

Sumegha Garg
  • Rutgers University, New Brunswick, NJ, USA
Songhua He
  • Rutgers University, New Brunswick, NJ, USA
Periklis A. Papakonstantinou
  • Rutgers University, New Brunswick, NJ, USA

Funding

  • He, Songhua: The author was partially supported by Karthik C. S. through the National Science Foundation under Grant CCF-2443697.

Acknowledgements

The authors would like to thank anonymous reviewers for their valuable suggestions. Songhua He would also like to thank Karthik C. S. for generously providing partial research fellowship.

References

  1. Nir Ailon, Moses Charikar, and Alantha Newman. Aggregating inconsistent information: ranking and clustering. Journal of the ACM (JACM), 55(5):1-27, 2008. URL: https://doi.org/10.1145/1411509.1411513.
  2. 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. URL: https://doi.org/10.1137/07067917X.
  3. Sepehr Assadi, Vaggos Chatziafratis, Jakub Lacki, Vahab Mirrokni, and Chen Wang. Hierarchical clustering in graph streams: Single-pass algorithms and space lower bounds. In Po-Ling Loh and Maxim Raginsky, editors, Conference on Learning Theory, 2-5 July 2022, London, UK, volume 178 of Proceedings of Machine Learning Research, pages 4643-4702. PMLR, PMLR, 2022. URL: https://proceedings.mlr.press/v178/assadi22a.html.
  4. Sepehr Assadi, Vihan Shah, and Chen Wang. Streaming algorithms and lower bounds for estimating correlation clustering cost. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine, editors, Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 - 16, 2023, volume 36, pages 75201-75213, 2023. URL: http://papers.nips.cc/paper_files/paper/2023/hash/ee1a1ecc92f35702b5c29dad3dc909ea-Abstract-Conference.html.
  5. Sepehr Assadi and Chen Wang. Sublinear time and space algorithms for correlation clustering via sparse-dense decompositions. In Mark Braverman, editor, 13th Innovations in Theoretical Computer Science Conference, ITCS 2022, Berkeley, CA, USA, January 31 - February 3, 2022, volume 215 of LIPIcs, pages 10:1-10:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ITCS.2022.10.
  6. Nikhil Bansal, Avrim Blum, and Shuchi Chawla. Correlation clustering. Machine Learning, 56:89-113, 2004. URL: https://doi.org/10.1023/B:MACH.0000033116.57574.95.
  7. Soheil Behnezhad, Moses Charikar, Weiyun Ma, and Li-Yang Tan. Almost 3-approximate correlation clustering in constant rounds. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 720-731. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00074.
  8. Soheil Behnezhad, Moses Charikar, Weiyun Ma, and Li-Yang Tan. Single-pass streaming algorithms for correlation clustering. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 819-849. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch33.
  9. Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Cliff Stein, and Madhu Sudan. Fully dynamic maximal independent set with polylogarithmic update time. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), pages 382-405. IEEE, 2019. URL: https://doi.org/10.1109/FOCS.2019.00032.
  10. Aditya Bhaskara, Samira Daruki, and Suresh Venkatasubramanian. Sublinear algorithms for MAXCUT and correlation clustering. In Ioannis Chatzigiannakis, Christos Kaklamanis, Dániel Marx, and Donald Sannella, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, Prague, Czech Republic, July 9-13, 2018, volume 107 of LIPIcs, pages 16:1-16:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ICALP.2018.16.
  11. Marco Bressan, Nicolò Cesa-Bianchi, Andrea Paudice, and Fabio Vitale. Correlation clustering with adaptive similarity queries. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d'Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, volume 32, pages 12510-12519, 2019. URL: https://proceedings.neurips.cc/paper/2019/hash/b0ba5c44aaf65f6ca34cf116e6d82ebf-Abstract.html.
  12. Mélanie Cambus, Fabian Kuhn, Etna Lindy, Shreyas Pai, and Jara Uitto. A (3+ε)-approximate correlation clustering algorithm in dynamic streams. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2861-2880. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.101.
  13. Nairen Cao, Vincent Cohen-Addad, Euiwoong Lee, Shi Li, David Rasmussen Lolck, Alantha Newman, Mikkel Thorup, Lukas Vogl, Shuyi Yan, and Hanwen Zhang. Solving the correlation cluster lp in sublinear time. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC), pages 1154-1165, 2025. URL: https://doi.org/10.1145/3717823.3718181.
  14. Nairen Cao, Vincent Cohen-Addad, Euiwoong Lee, Shi Li, Alantha Newman, and Lukas Vogl. Understanding the cluster linear program for correlation clustering. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC), pages 1605-1616, 2024. URL: https://doi.org/10.1145/3618260.3649749.
  15. Nairen Cao, Shang-En Huang, and Hsin-Hao Su. Breaking 3-factor approximation for correlation clustering in polylogarithmic rounds. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 4124-4154. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.143.
  16. Moses Charikar, Venkatesan Guruswami, and Anthony Wirth. Clustering with qualitative information. Journal of Computer and System Sciences, 71(3):360-383, 2005. URL: https://doi.org/10.1016/j.jcss.2004.10.012.
  17. Shuchi Chawla, Konstantin Makarychev, Tselil Schramm, and Grigory Yaroslavtsev. Near optimal lp rounding algorithm for correlationclustering on complete and complete k-partite graphs. In Proceedings of the 47th annual ACM Symposium on Theory of Computing (STOC), pages 219-228, 2015. URL: https://doi.org/10.1145/2746539.2746604.
  18. Chi-Ning Chou, Alexander Golovnev, and Santhoshini Velusamy. Optimal streaming approximations for all boolean max-2csps and max-ksat. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 330-341. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00039.
  19. Fan RK Chung, Ronald L Graham, Peter Frankl, and James B Shearer. Some intersection theorems for ordered sets and graphs. Journal of Combinatorial Theory, Series A, 43(1):23-37, 1986. URL: https://doi.org/10.1016/0097-3165(86)90019-1.
  20. Vincent Cohen-Addad, Silvio Lattanzi, Slobodan Mitrović, Ashkan Norouzi-Fard, Nikos Parotsidis, and Jakub Tarnawski. Correlation clustering in constant many parallel rounds. In International Conference on Machine Learning (ICML), pages 2069-2078. PMLR, 2021. URL: http://proceedings.mlr.press/v139/cohen-addad21b.html.
  21. Vincent Cohen-Addad, Euiwoong Lee, Shi Li, and Alantha Newman. Handling correlated rounding error via preclustering: A 1.73-approximation for correlation clustering. In IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 1082-1104. IEEE, 2023. URL: https://doi.org/10.1109/FOCS57990.2023.00065.
  22. Vincent Cohen-Addad, Euiwoong Lee, and Alantha Newman. Correlation clustering with sherali-adams. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 651-661. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00068.
  23. Vincent Cohen-Addad, David Rasmussen Lolck, Marcin Pilipczuk, Mikkel Thorup, Shuyi Yan, and Hanwen Zhang. Combinatorial correlation clustering. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC), pages 1617-1628, 2024. URL: https://doi.org/10.1145/3618260.3649712.
  24. Itai Dinur. Time-space lower bounds for bounded-error computation in the random-query model. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2900-2915. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.103.
  25. Yumou Fei, Dor Minzer, and Shuo Wang. Multi-pass streaming lower bounds for approximating max-cut. 66th IEEE Symposium on Foundations of Computer Science (FOCS) 2025, 2025. Google Scholar
  26. Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, and Ronald De Wolf. Exponential separations for one-way quantum communication complexity, with applications to cryptography. In Proceedings of the 39th Annual ACM Symposium on Theory of Computing (STOC), pages 516-525, 2007. URL: https://doi.org/10.1145/1250790.1250866.
  27. Venkatesan Guruswami and Runzhou Tao. Streaming hardness of unique games. In Dimitris Achlioptas and László A. Végh, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019, Massachusetts Institute of Technology, Cambridge, MA, USA, September 20-22, 2019, volume 145 of LIPIcs, pages 5:1-5:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.5.
  28. Venkatesan Guruswami, Ameya Velingker, and Santhoshini Velusamy. Streaming complexity of approximating max 2csp and max acyclic subgraph. In Klaus Jansen, José D. P. Rolim, David Williamson, and Santosh S. Vempala, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2017, Berkeley, CA, USA, August 16-18, 2017, volume 81 of LIPIcs, pages 8:1-8:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.8.
  29. John Kallaugher, Michael Kapralov, and Eric Price. The sketching complexity of graph and hypergraph counting. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 556-567. IEEE, 2018. URL: https://doi.org/10.1109/FOCS.2018.00059.
  30. Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. Approximating matching size from random streams. In Proceedings of the 25th annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 734-751. SIAM, 2014. URL: https://doi.org/10.1137/1.9781611973402.55.
  31. Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. Streaming lower bounds for approximating MAX-CUT. In Piotr Indyk, editor, Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 1263-1282. SIAM, SIAM, 2015. URL: https://doi.org/10.1137/1.9781611973730.84.
  32. Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. (1+ ω (1))-approximation to max-cut requires linear space. In Philip N. Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1703-1722. SIAM, SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.112.
  33. Tali Kaufman, Michael Krivelevich, and Dana Ron. Tight bounds for testing bipartiteness in general graphs. SIAM Journal on Computing, 33(6):1441-1483, 2004. URL: https://doi.org/10.1137/S0097539703436424.
  34. Dmitry Kogan and Robert Krauthgamer. Sketching cuts in graphs and hypergraphs. In 6th Conference on Innovations in Theoretical Computer Science (ITCS), pages 367-376, 2015. URL: https://doi.org/10.1145/2688073.2688093.
  35. Konstantin Makarychev and Sayak Chakrabarty. Single-pass pivot algorithm for correlation clustering. keep it simple! In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine, editors, Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 - 16, 2023, volume 36, pages 6412-6421, 2023. URL: http://papers.nips.cc/paper_files/paper/2023/hash/149ad6e32c08b73a3ecc3d11977fcc47-Abstract-Conference.html.
  36. Ran Raz and Wei Zhan. The random-query model and the memory-bounded coupon collector. In Thomas Vidick, editor, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, Seattle, Washington, USA, January 12-14, 2020, volume 151 of LIPIcs, pages 20:1-20:11. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.20.
  37. Elad Verbin and Wei Yu. The streaming complexity of cycle counting, sorting by reversals, and other problems. In Proceedings of the 22nd annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 11-25. SIAM, 2011. URL: https://doi.org/10.1137/1.9781611973082.2.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact