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We give a polynomial-time constant-factor approximation algorithm for maximumindependent set for (axis-aligned) rectangles in the plane. Using apolynomial-time algorithm, the best approximation factor previously known is$O(\log\log n)$. The results are based on a new form of recursive partitioningin the plane, in which faces that are constant-complexity and orthogonallyconvex are recursively partitioned into a constant number of such faces.

Approximating Maximum Independent Set for Rectangles in the Plane