Faster Global Minimum Cut with Predictions

Helia Niaparast, Benjamin Moseley, Karan Singh
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:46305-46319, 2025.

Abstract

Global minimum cut is a fundamental combinatorial optimization problem with wide-ranging applications. Often in practice, these problems are solved repeatedly on families of similar or related instances. However, the de facto algorithmic approach is to solve each instance of the problem from scratch discarding information from prior instances. In this paper, we consider how predictions informed by prior instances can be used to warm-start practical minimum cut algorithms. The paper considers the widely used Karger’s algorithm and its counterpart, the Karger-Stein algorithm. Given good predictions, we show these algorithms become near-linear time and have robust performance to erroneous predictions. Both of these algorithms are randomized edge-contraction algorithms. Our natural idea is to probabilistically prioritize the contraction of edges that are unlikely to be in the minimum cut.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-niaparast25a, title = {Faster Global Minimum Cut with Predictions}, author = {Niaparast, Helia and Moseley, Benjamin and Singh, Karan}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {46305--46319}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/niaparast25a/niaparast25a.pdf}, url = {https://proceedings.mlr.press/v267/niaparast25a.html}, abstract = {Global minimum cut is a fundamental combinatorial optimization problem with wide-ranging applications. Often in practice, these problems are solved repeatedly on families of similar or related instances. However, the de facto algorithmic approach is to solve each instance of the problem from scratch discarding information from prior instances. In this paper, we consider how predictions informed by prior instances can be used to warm-start practical minimum cut algorithms. The paper considers the widely used Karger’s algorithm and its counterpart, the Karger-Stein algorithm. Given good predictions, we show these algorithms become near-linear time and have robust performance to erroneous predictions. Both of these algorithms are randomized edge-contraction algorithms. Our natural idea is to probabilistically prioritize the contraction of edges that are unlikely to be in the minimum cut.} }
Endnote
%0 Conference Paper %T Faster Global Minimum Cut with Predictions %A Helia Niaparast %A Benjamin Moseley %A Karan Singh %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-niaparast25a %I PMLR %P 46305--46319 %U https://proceedings.mlr.press/v267/niaparast25a.html %V 267 %X Global minimum cut is a fundamental combinatorial optimization problem with wide-ranging applications. Often in practice, these problems are solved repeatedly on families of similar or related instances. However, the de facto algorithmic approach is to solve each instance of the problem from scratch discarding information from prior instances. In this paper, we consider how predictions informed by prior instances can be used to warm-start practical minimum cut algorithms. The paper considers the widely used Karger’s algorithm and its counterpart, the Karger-Stein algorithm. Given good predictions, we show these algorithms become near-linear time and have robust performance to erroneous predictions. Both of these algorithms are randomized edge-contraction algorithms. Our natural idea is to probabilistically prioritize the contraction of edges that are unlikely to be in the minimum cut.
APA
Niaparast, H., Moseley, B. & Singh, K.. (2025). Faster Global Minimum Cut with Predictions. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:46305-46319 Available from https://proceedings.mlr.press/v267/niaparast25a.html.

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