Abstract. In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family R = {R 1 , . . . , R n } 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 R. 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.
Chepoi and Felsner REF proposed 6-approximation polynomial time algorithm for the case of axis-parallel rectangles intersected by an axis-monotone Lagrangian curve.
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve
Comput. Geom.
Comput. Geom.
Computer Science Mathematics