  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.
