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Near-Optimal Streaming Approximation for Max-DICUT in Sublinear Space Using Two Passes

Author Santhoshini Velusamy

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Streaming models
Keywords
  • Streaming algorithms
  • Approximation algorithms
  • Graph algorithms

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Abstract

The Max-DICUT problem has emerged as a canonical problem for understanding the approximability of constraint satisfaction problems in the streaming model. A seminal result of Kapralov and Krachun [STOC 2019] shows that it is impossible to beat 1/2-approximation for Max-DICUT in sublinear space in the single-pass streaming setting, even on bounded-degree graphs. In a recent work, Saxena, Singer, Sudan, and Velusamy [SODA 2025] prove that the above lower bound is tight by giving a single-pass algorithm for bounded-degree graphs that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0. For arbitrary graphs of unbounded degree, they give an O(1/ε)-pass O(log n) space algorithm. Their work left open the question of obtaining 1/2-approximation for arbitrary graphs in the single-pass setting in sublinear space. We make progress towards this question and give a two-pass algorithm that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0.

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Santhoshini Velusamy. Near-Optimal Streaming Approximation for Max-DICUT in Sublinear Space Using Two Passes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.4

Author Details

Santhoshini Velusamy
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada

Funding

  • Velusamy, Santhoshini: Supported in part by NSF award CCF-2348475 when the author was affiliated with Toyota Technological Institute at Chicago.

Acknowledgements

Part of the work was conducted when the author was visiting the Simons Institute for the Theory of Computing as a research fellow in the Sublinear Algorithms program. The author thanks Raghuvansh Saxena, Noah Singer, and Madhu Sudan for collaborating on earlier investigations into this problem. The author thanks Aditya Bhaskara for discussions related to [Aditya Bhaskara et al., 2018]. The author also thanks Sergio Thoumi for pointing out typos in a previous version.

References

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