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+2d(d-1))n/n3/2).
Bibliographical noteFunding Information:
✩ Work on this paper by the first and second authors has been supported in part by AIM@SHAPE, a grant of the European Commission 6th Framework. * Corresponding author. E-mail addresses: email@example.com (E. Ackerman), firstname.lastname@example.org (G. Barequet), email@example.com (R.Y. Pinter), firstname.lastname@example.org (D. Romik).
- Binary space partitions
- Combinatorial problems
- Guillotine partitions
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications