Pruned Pivot: Correlation Clustering Algorithm for Dynamic, Parallel, and Local Computation Models

Mina Dalirrooyfard, Konstantin Makarychev, Slobodan Mitrovic
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:9931-9952, 2024.

Abstract

Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many applications in data mining, particularly in unsupervised learning. Inspired by the prevalence of large graphs and constantly changing data in modern applications, we study correlation clustering in dynamic, parallel (MPC), and local computation (LCA) settings. We design an approach that improves state-of-the-art runtime complexities in all these settings. In particular, we provide the first fully dynamic algorithm that runs in an expected amortized constant time, without any dependence on the graph size. Moreover, our algorithm essentially matches the approximation guarantee of the celebrated Pivot algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-dalirrooyfard24a, title = {Pruned Pivot: Correlation Clustering Algorithm for Dynamic, Parallel, and Local Computation Models}, author = {Dalirrooyfard, Mina and Makarychev, Konstantin and Mitrovic, Slobodan}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {9931--9952}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/dalirrooyfard24a/dalirrooyfard24a.pdf}, url = {https://proceedings.mlr.press/v235/dalirrooyfard24a.html}, abstract = {Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many applications in data mining, particularly in unsupervised learning. Inspired by the prevalence of large graphs and constantly changing data in modern applications, we study correlation clustering in dynamic, parallel (MPC), and local computation (LCA) settings. We design an approach that improves state-of-the-art runtime complexities in all these settings. In particular, we provide the first fully dynamic algorithm that runs in an expected amortized constant time, without any dependence on the graph size. Moreover, our algorithm essentially matches the approximation guarantee of the celebrated Pivot algorithm.} }
Endnote
%0 Conference Paper %T Pruned Pivot: Correlation Clustering Algorithm for Dynamic, Parallel, and Local Computation Models %A Mina Dalirrooyfard %A Konstantin Makarychev %A Slobodan Mitrovic %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-dalirrooyfard24a %I PMLR %P 9931--9952 %U https://proceedings.mlr.press/v235/dalirrooyfard24a.html %V 235 %X Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many applications in data mining, particularly in unsupervised learning. Inspired by the prevalence of large graphs and constantly changing data in modern applications, we study correlation clustering in dynamic, parallel (MPC), and local computation (LCA) settings. We design an approach that improves state-of-the-art runtime complexities in all these settings. In particular, we provide the first fully dynamic algorithm that runs in an expected amortized constant time, without any dependence on the graph size. Moreover, our algorithm essentially matches the approximation guarantee of the celebrated Pivot algorithm.
APA
Dalirrooyfard, M., Makarychev, K. & Mitrovic, S.. (2024). Pruned Pivot: Correlation Clustering Algorithm for Dynamic, Parallel, and Local Computation Models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:9931-9952 Available from https://proceedings.mlr.press/v235/dalirrooyfard24a.html.

Related Material