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Learning-Augmented Streaming Algorithms for Approximating MAX-CUT

Authors Yinhao Dong , Pan Peng , Ali Vakilian

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Author Details

Yinhao Dong
  • School of Computer Science and Technology, University of Science and Technology of China, Hefei, China
Pan Peng
  • School of Computer Science and Technology, University of Science and Technology of China, Hefei, China
Ali Vakilian
  • Toyota Technological Institute at Chicago (TTIC), IL, USA

Funding

The work was conducted in part while Pan Peng and Ali Vakilian were long-term visitors at the Simons Institute for the Theory of Computing as part of the Sublinear Algorithms program. Yinhao Dong and Pan Peng are supported in part by NSFC grant 62272431.

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Yinhao Dong, Pan Peng, and Ali Vakilian. Learning-Augmented Streaming Algorithms for Approximating MAX-CUT. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 44:1-44:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.44

Abstract

We study learning-augmented streaming algorithms for estimating the value of MAX-CUT in a graph. In the classical streaming model, while a 1/2-approximation for estimating the value of MAX-CUT can be trivially achieved with O(1) words of space, Kapralov and Krachun [STOC’19] showed that this is essentially the best possible: for any ε > 0, any (randomized) single-pass streaming algorithm that achieves an approximation ratio of at least 1/2 + ε requires Ω(n / 2^poly(1/ε)) space.
We show that it is possible to surpass the 1/2-approximation barrier using just O(1) words of space by leveraging a (machine learned) oracle. Specifically, we consider streaming algorithms that are equipped with an ε-accurate oracle that for each vertex in the graph, returns its correct label in {-1, +1}, corresponding to an optimal MAX-CUT solution in the graph, with some probability 1/2 + ε, and the incorrect label otherwise. 
Within this framework, we present a single-pass algorithm that approximates the value of MAX-CUT to within a factor of 1/2 + Ω(ε²) with probability at least 2/3 for insertion-only streams, using only poly(1/ε) words of space. We also extend our algorithm to fully dynamic streams while maintaining a space complexity of poly(1/ε,log n) words.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Learning-Augmented Algorithms
  • Graph Streaming Algorithms
  • MAX-CUT

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