Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve

In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family R={R1,…,Rn}R={R1,…,Rn} of axis-parallel rectangles in the plane such that there exists an axis-monotone curve γ   that intersects each rectangle in the family. The quality of the hitting set is shown by comparing it to the size of a packing (set of pairwise non-intersecting rectangles) that is constructed along, hence, we also obtain a factor 6 approximation for the maximum packing of RR.In cases where the axis-monotone curve γ intersects the same side (e.g. the bottom side) of each rectangle in the family the approximation factor for hitting set and packing is 3.