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

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Abstract

In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family 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 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. © 2013 Elsevier B.V.

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Chepoi, V., & Felsner, S. (2013). Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve. Computational Geometry: Theory and Applications, 46(9), 1036–1041. https://doi.org/10.1016/j.comgeo.2013.05.008

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