Document Open Access Logo

Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering

Authors Nairen Cao , Shi Li , Jia Ye

PDF HTML 5

Files

Thumbnail PDF
PDF
LIPIcs.ICALP.2025.40.pdf
  • Filesize: 0.88 MB
  • 20 pages
HTML5 Logo HTML (experimental)
LIPIcs.ICALP.2025.40.html

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Massively parallel algorithms
Keywords
  • Correlation Clustering
  • All-Norms
  • Approximation Algorithm
  • Massively Parallel Algorithm

Metrics

Abstract

We revisit the simultaneous approximation model for the correlation clustering problem introduced by Davies, Moseley, and Newman [Davies et al., 2024]. The objective is to find a clustering that minimizes given norms of the disagreement vector over all vertices. 
We present an efficient algorithm that produces a clustering that is simultaneously a 63.3-approximation for all monotone symmetric norms. This significantly improves upon the previous approximation ratio of 6348 due to Davies, Moseley, and Newman [Davies et al., 2024], which works only for 𝓁_p-norms. 
To achieve this result, we first reduce the problem to approximating all top-k norms simultaneously, using the connection between monotone symmetric norms and top-k norms established by Chakrabarty and Swamy [Chakrabarty and Swamy, 2019]. Then we develop a novel procedure that constructs a 12.66-approximate fractional clustering for all top-k norms. Our 63.3-approximation ratio is obtained by combining this with the 5-approximate rounding algorithm by Kalhan, Makarychev, and Zhou [Kalhan et al., 2019].
We then demonstrate that with a loss of ε in the approximation ratio, the algorithm can be adapted to run in nearly linear time and in the MPC (massively parallel computation) model with poly-logarithmic number of rounds. 
By allowing a further trade-off in the approximation ratio to (359+ε), the number of MPC rounds can be reduced to a constant.

Cite As Get BibTex

Nairen Cao, Shi Li, and Jia Ye. Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.40

Author Details

Nairen Cao
  • Department of Computer Science and Engineering, New York University, NY, USA
Shi Li
  • School of Computer Science, Nanjing University, China
Jia Ye
  • School of Computer Science, Nanjing University, China

Funding

  • Cao, Nairen: Supported by NSF grant CCF-2008422.
  • Li, Shi: Supported by the State Key Laboratory for Novel Software Technology, and the New Cornerstone Science Laboratory.
  • Ye, Jia: Supported by the State Key Laboratory for Novel Software Technology, and the New Cornerstone Science Laboratory.

References

  1. Rakesh Agrawal, Alan Halverson, Krishnaram Kenthapadi, Nina Mishra, and Panayiotis Tsaparas. Generating labels from clicks. In Proceedings of the Second ACM International Conference on Web Search and Data Mining, pages 172-181, 2009. URL: https://doi.org/10.1145/1498759.1498824.
  2. Nir Ailon, Moses Charikar, and Alantha Newman. Aggregating inconsistent information: Ranking and clustering. Journal of the ACM, 55(5):1-27, 2008. URL: https://doi.org/10.1145/1411509.1411513.
  3. Sepehr Assadi and Chen Wang. Sublinear time and space algorithms for correlation clustering via sparse-dense decompositions. In Proceedings of the 13th Conference on Innovations in Theoretical Computer Science (ITCS), volume 215 of LIPIcs, pages 10:1-10:20, 2022. URL: https://doi.org/10.4230/LIPICS.ITCS.2022.10.
  4. Nikhil Bansal, Avrim Blum, and Shuchi Chawla. Correlation clustering. Machine learning, 56(1):89-113, 2004. URL: https://doi.org/10.1023/B:MACH.0000033116.57574.95.
  5. Guy E Blelloch, Jeremy T Fineman, and Julian Shun. Greedy sequential maximal independent set and matching are parallel on average. In Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures, pages 308-317, 2012. URL: https://doi.org/10.1145/2312005.2312058.
  6. Mélanie Cambus, Davin Choo, Havu Miikonen, and Jara Uitto. Massively parallel correlation clustering in bounded arboricity graphs. In 35th International Symposium on Distributed Computing (DISC), volume 209 of LIPIcs, pages 15:1-15:18, 2021. URL: https://doi.org/10.4230/LIPICS.DISC.2021.15.
  7. 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.
  8. 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, pages 1605-1616, 2024. URL: https://doi.org/10.1145/3618260.3649749.
  9. 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.
  10. Deepayan Chakrabarti, Ravi Kumar, and Kunal Punera. A graph-theoretic approach to webpage segmentation. In Proceedings of the 17th International conference on World Wide Web (WWW), pages 377-386, 2008. URL: https://doi.org/10.1145/1367497.1367549.
  11. Deeparnab Chakrabarty and Chaitanya Swamy. Approximation algorithms for minimum norm and ordered optimization problems. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 126-137, 2019. URL: https://doi.org/10.1145/3313276.3316322.
  12. Moses Charikar, Neha Gupta, and Roy Schwartz. Local guarantees in graph cuts and clustering. In International Conference on Integer Programming and Combinatorial Optimization (IPCO), pages 136-147, 2017. URL: https://doi.org/10.1007/978-3-319-59250-3_12.
  13. 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.
  14. Shuchi Chawla, Konstantin Makarychev, Tselil Schramm, and Grigory Yaroslavtsev. Near optimal LP rounding algorithm for correlation clustering 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.
  15. Yudong Chen, Sujay Sanghavi, and Huan Xu. Clustering sparse graphs. In Advances in Neural Information Processing Systems (Neurips), pages 2204-2212, 2012. Google Scholar
  16. Flavio Chierichetti, Nilesh Dalvi, and Ravi Kumar. Correlation clustering in MapReduce. In Proceedings of the 20th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), pages 641-650, 2014. URL: https://doi.org/10.1145/2623330.2623743.
  17. 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, pages 2069-2078. PMLR, 2021. URL: http://proceedings.mlr.press/v139/cohen-addad21b.html.
  18. Vincent Cohen-Addad, Euiwoong Lee, Shi Li, and Alantha Newman. Handling correlated rounding error via preclustering: A 1.73-approximation for correlation clustering. In Proceedings of the 64rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2023. Google Scholar
  19. Vincent Cohen-Addad, Euiwoong Lee, and Alantha Newman. Correlation clustering with Sherali-Adams. In Proceedings of 63rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 651-661, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00068.
  20. Sami Davies, Benjamin Moseley, and Heather Newman. Fast combinatorial algorithms for min max correlation clustering. arXiv preprint arXiv:2301.13079, 2023. URL: https://doi.org/10.48550/arXiv.2301.13079.
  21. Sami Davies, Benjamin Moseley, and Heather Newman. Simultaneously approximating all lp-norms in correlation clustering. In 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024, 2024. Google Scholar
  22. Jeffrey Dean and Sanjay Ghemawat. Mapreduce: simplified data processing on large clusters. Communications of the ACM, 51(1):107-113, 2008. URL: https://doi.org/10.1145/1327452.1327492.
  23. Manuela Fischer and Andreas Noever. Tight analysis of parallel randomized greedy mis. ACM Transactions on Algorithms (TALG), 16(1):1-13, 2019. URL: https://doi.org/10.1145/3326165.
  24. Holger SG Heidrich, Jannik Irmai, and Bjoern Andres. A 4-approximation algorithm for min max correlation clustering. In AISTATS, pages 1945-1953, 2024. Google Scholar
  25. Dmitri V. Kalashnikov, Zhaoqi Chen, Sharad Mehrotra, and Rabia Nuray-Turan. Web people search via connection analysis. IEEE Transactions on Knowledge and Data Engineering, 20(11):1550-1565, 2008. URL: https://doi.org/10.1109/TKDE.2008.78.
  26. Sanchit Kalhan, Konstantin Makarychev, and Timothy Zhou. Correlation clustering with local objectives. Advances in Neural Information Processing Systems, 32, 2019. Google Scholar
  27. Michael Luby. A simple parallel algorithm for the maximal independent set problem. In Proceedings of the seventeenth annual ACM symposium on Theory of computing, pages 1-10, 1985. URL: https://doi.org/10.1145/22145.22146.
  28. Xinghao Pan, Dimitris S. Papailiopoulos, Samet Oymak, Benjamin Recht, Kannan Ramchandran, and Michael I. Jordan. Parallel correlation clustering on big graphs. In Advances in Neural Information Processing Systems (Neurips), pages 82-90, 2015. URL: https://proceedings.neurips.cc/paper/2015/hash/b53b3a3d6ab90ce0268229151c9bde11-Abstract.html.
  29. Gregory Puleo and Olgica Milenkovic. Correlation clustering and biclustering with locally bounded errors. In International Conference on Machine Learning, pages 869-877. PMLR, 2016. URL: http://proceedings.mlr.press/v48/puleo16.html.
  30. Jessica Shi, Laxman Dhulipala, David Eisenstat, Jakub Łkacki, and Vahab Mirrokni. Scalable community detection via parallel correlation clustering. arXiv preprint arXiv:2108.01731, 2021. Google Scholar
  31. Nate Veldt, David F. Gleich, and Anthony Wirth. A correlation clustering framework for community detection. In Proceedings of the 2018 ACM World Wide Web Conference (WWW), pages 439-448, 2018. URL: https://doi.org/10.1145/3178876.3186110.
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