research-article

Approximate Graph Colouring and the Hollow Shadow

Authors:
Lorenzo Ciardo

University of Oxford, UK

University of Oxford, UK
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,
Stanislav Živný

University of Oxford, UK

University of Oxford, UK
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STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of ComputingJune 2023Pages 623–631https://doi.org/10.1145/3564246.3585112

Published:02 June 2023Publication History

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

Pages 623–631

ABSTRACT

We show that approximate graph colouring is not solved by constantly many levels of the lift-and-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.

References

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Index Terms

Approximate Graph Colouring and the Hollow Shadow
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms
    1. Approximation algorithms analysis

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STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing
June 2023
1926 pages
ISBN:9781450399135
DOI:10.1145/3564246
General Chair:
Barna Saha
University of California at San Diego, USA
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Columbia University, USA
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Diophantine equations
Sherali-Adams linear programming relaxations
affine integer programming relaxations
approximate graph colouring
promise constraint satisfaction
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Approximate Graph Colouring and the Hollow Shadow

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

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Approximate graph coloring by semidefinite programming

Approximate graph coloring by semidefinite programming

Graph colouring via the discharging method

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Approximate Graph Colouring and the Hollow Shadow

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

ABSTRACT

References

Cited By

Index Terms

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Approximate graph coloring by semidefinite programming

Approximate graph coloring by semidefinite programming

Graph colouring via the discharging method

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