Label placement by maximum independent set in rectangles

Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can nd an O(logn)-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit height, we can nd a 2-approximation in O(n logn) time. Extending this result, we obtain a (1 + 1 k )-approximation in time O(n logn + n ) time, for any integer k 1.