On the union complexity of families of axis-parallel rectangles with a low packing number Academic Article uri icon

abstract

  • Abstract: Let R be a family of n axis-parallel rectangles with packing number p-1, meaning that among any p of the rectangles, there are two with a non-empty intersection. We show that the union complexity of R is at most O (n+ p^ 2), and that the (<= k)-level complexity of R is at most O (kn+ k^ 2p^ 2). Both upper bounds are tight.

publication date

  • January 1, 2017

published in