Approximability and hardness of geometric hitting set with axis-parallel rectangles

Abstract

We show that geometric hitting set with axis-parallel rectangles is -hard even when all rectangles share a common point. We also show that geometric hitting set problem is -hard for several classes of objects given in [3] such as axis-parallel ellipses with a shared point, axis-parallel cubes sharing a common point, etc.

Further, we give a polynomial time approximation scheme () for the weighted hitting set problem with axis-parallel rectangles when all rectangles have integer side lengths bounded by a constant C. Finally, we show that the problem is -hard for rectangles of size and even when every rectangle intersects a given unit height horizontal strip.