Approximating Maximum Independent Set for Rectangles in the Plane

TL;DR

This paper presents a polynomial-time algorithm that approximates the maximum independent set of axis-aligned rectangles in the plane within a constant factor, improving upon the previous $O(\log\log n)$ approximation.

Contribution

It introduces a novel recursive partitioning method that enables a constant-factor approximation for the problem, a significant improvement over prior logarithmic approximations.

Findings

Achieved a polynomial-time constant-factor approximation algorithm.

Developed a new recursive partitioning technique for faces in the plane.

Improved the approximation factor from $O(\log\log n)$ to a constant.

Abstract

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 into a constant number of such faces.