Label Placement by Maximum Independent Set in Rectangles

Pankaj K. Agarwal, Marc Van Kreveld, Subhash Suri


Motivated by the problem of labeling maps, we investiage 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 >= 1.