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Learning-Augmented Maximum Independent Set

Authors Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, Chen Wang

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  • Theory of computation → Graph algorithms analysis
  • Computing methodologies → Machine learning
Keywords
  • Learning-augmented algorithms
  • maximum independent set
  • graph algorithms

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Abstract

We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n^(1-δ) for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2+ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Õ((√Δ)/ε)-approximation in O(m) time where Δ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε²) total queries and Õ(m) runtime.

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Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang. Learning-Augmented Maximum Independent Set. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.24

Author Details

Vladimir Braverman
  • Rice University, Houston, TX, USA
  • Google Research
Prathamesh Dharangutte
  • Rutgers University, NJ, USA
Vihan Shah
  • University of Waterloo, ON, Canada
Chen Wang
  • Rice University, Houston, TX, USA
  • Texas A&M University, College Station, TX, USA

Funding

  • Braverman, Vladimir: Supported partially by the Naval Research (ONR) grant N00014-23-1-2737, and NSF-CNS 2333887 award.
  • Dharangutte, Prathamesh: Supported by NSF through IIS-2229876 and CCF-2118953.
  • Shah, Vihan: Supported in part by Sepehr Assadi’s Sloan Research Fellowship and NSERC Discovery Grant.

Acknowledgements

The authors are grateful to Sepehr Assadi and Samson Zhou for the helpful conversations regarding the project. The authors also thank anonymous APPROX reviewers for helpful suggestions.

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