The number of guillotine partitions in d dimensions
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 Theta((2d - 1 + 2 root d-(d- 1))(n)/n(3)/(2)), root (c) 2006 Elsevier B.V. All rights reserved.
guillotine partitions combinatorial problems binary space partitions