Worst-case-optimal algorithms for guarding planar graphs and polyhedral surfaces
Computational Geometry: Theory and Applications
The number of guillotine partitions in d dimensions
Information Processing Letters
Polychromatic colorings of plane graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
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A strong hyperbox-respecting coloringof an n-dimensional hyperbox partition is a coloring of the corners of its hyperboxes with 2ncolors such that any hyperbox has all the colors appearing on its corners. A guillotine-partitionis obtained by starting with a single axis-parallel hyperbox and recursively cutting a hyperbox of the partition into two hyperboxes by a hyperplane orthogonal to one of the naxes. We prove that there is a strong hyperbox-respecting coloring of any n-dimensional guillotine-partition. This theorem generalizes the result of Horev et al. [8] who proved the 2-dimensional case. This problem is a special case of the n-dimensional variant of polychromatic colorings. The proof gives an efficient coloring algorithm as well.