论文信息 - The number of guillotine partitions in d dimensions

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 @Q((2d-1+2d(d-1))^n/n^3^/^2).

[1] Thomas Lengauer,et al. Combinatorial algorithms for integrated circuit layout , 1990, Applicable theory in computer science.

[2] Bruce F. Naylor,et al. Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.

[3] R. Stanley,et al. Algebraic enumeration , 1996 .

[4] Alade O. Tokuta. Motion planning using binary space partitioning , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[5] Ronald L. Graham,et al. Floorplan representations: Complexity and connections , 2003, TODE.

[6] Joseph S. B. Mitchell,et al. Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems , 1999, SIAM J. Comput..

[7] Teofilo F. Gonzalez,et al. Inproved Bounds for Rectangular and Guillotine Partitions , 1989, J. Symb. Comput..

[8] Henry Fuchs,et al. On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[9] R. Graham,et al. Handbook of Combinatorics , 1995 .

[10] Teofilo F. Gonzalez,et al. On Optimal Guillotine Partitions Approximating Optimal D-box Partitions , 1994, Comput. Geom..

[11] A. Odlyzko. Asymptotic enumeration methods , 1996 .

[12] Steven K. Feiner,et al. Near real-time shadow generation using BSP trees , 1989, SIGGRAPH '89.

[13] Charalambos A. Charalambides,et al. Enumerative combinatorics , 2018, SIGA.