Corpus ID: 230435887

Approximating Maximum Independent Set for Rectangles in the Plane

@article{Mitchell2021ApproximatingMI,
  title={Approximating Maximum Independent Set for Rectangles in the Plane},
  author={Joseph S. B. Mitchell},
  journal={ArXiv},
  year={2021},
  volume={abs/2101.00326}
}
We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is O(log log n). The results are based on a new form of recursive partitioning in the plane, in which faces that are constant-complexity and orthogonally convex are recursively partitioned in a constant number of such faces. 
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  • arXiv preprint arXiv:2101.00326,
  • 2021
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This paper presents a 4-approximation algorithm for MISR which is based on a similar recursive partitioning scheme, however, it uses a more general class of polygons—polygons that are horizontally or vertically convex—which allows it to provide an arguably simpler analysis and improve the approximation ratio. Expand
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