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 find an O(log n)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 find a 2-approximation in O(n log n) time. Extending this result, we obtain a (1 + 1/k)-approximation in time O(n log n + n(2k-1)) time, for any integer k greater than or equal to 1. (C) 1998 Elsevier Science B.V. All rights reserved.