Cut equivalence of d-dimensional guillotine partitions
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چکیده
منابع مشابه
Cut equivalence of d-dimensional guillotine partitions
A guillotine partition of a d-dimensional axis-aligned box B is a recursive partition of B by axis-aligned hyperplane cuts. The size of a guillotine partition is the number of boxes it contains. Two guillotine partitions are box-equivalent if their boxes satisfy compatible order relations with respect to the axes. (In many works, box-equivalent guillotine partitions are considered identical.) I...
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Guillotine partitions play an important role in many research areas and application domains, e.g., computational geometry, computer graphics, integrated circuit layout, and solid modeling, to mention just a few. In this paper we present an exact summation formula for the number of structurally-different guillotine partitions in d dimensions by n hyperplanes, and then show that it is Θ (( 2d− 1 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.05.014