The number of guillotine partitions in d dimensions

Eyal Ackerman; Gill Barequet; Ron Y. Pinter; Dan Romik

doi:10.1016/j.ipl.2006.01.011

The number of guillotine partitions in d dimensions

Eyal Ackerman
, Gill Barequet
, Ron Y. Pinter
, Dan Romik

Research output: Contribution to journal › Article › peer-review

Abstract

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).

Original language	English
Pages (from-to)	162-167
Number of pages	6
Journal	Information Processing Letters
Volume	98
Issue number	4
DOIs	https://doi.org/10.1016/j.ipl.2006.01.011
State	Published - 31 May 2006
Externally published	Yes

Bibliographical note

Funding 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 protected] (E. Ackerman), [email protected] (G. Barequet), [email protected] (R.Y. Pinter), [email protected] (D. Romik).

Keywords

Binary space partitions
Combinatorial problems
Guillotine partitions

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2006.01.011

Cite this

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title = "The number of guillotine partitions in d dimensions",

abstract = "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).",

keywords = "Binary space partitions, Combinatorial problems, Guillotine partitions",

author = "Eyal Ackerman and Gill Barequet and Pinter, \{Ron Y.\} and Dan Romik",

note = "Funding 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 protected] (E. Ackerman), [email protected] (G. Barequet), [email protected] (R.Y. Pinter), [email protected] (D. Romik).",

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AU - Ackerman, Eyal

AU - Barequet, Gill

AU - Pinter, Ron Y.

AU - Romik, Dan

N1 - Funding 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 protected] (E. Ackerman), [email protected] (G. Barequet), [email protected] (R.Y. Pinter), [email protected] (D. Romik).

PY - 2006/5/31

Y1 - 2006/5/31

N2 - 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).

AB - 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).

KW - Binary space partitions

KW - Combinatorial problems

KW - Guillotine partitions

UR - https://www.scopus.com/pages/publications/33644888012

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DO - 10.1016/j.ipl.2006.01.011

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EP - 167

JO - Information Processing Letters

JF - Information Processing Letters

IS - 4

ER -

The number of guillotine partitions in d dimensions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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