Cut equivalence of d-dimensional guillotine partitions

Andrei Asinowski; Gill Barequet; Toufik Mansour; Ron Y. Pinter

doi:10.1016/j.disc.2014.05.014

Cut equivalence of d-dimensional guillotine partitions

Andrei Asinowski, Gill Barequet, Toufik Mansour, Ron Y. Pinter

Department of Mathematics

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

Abstract

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.) In the present work we define cut-equivalence of guillotine partitions, derived in a similar way from order relations of cuts. We prove structural properties related to these kinds of equivalence, and enumerate cut-equivalence classes of d-dimensional guillotine partitions of size n.

Original language	English
Pages (from-to)	165-174
Number of pages	10
Journal	Discrete Mathematics
Volume	331
DOIs	https://doi.org/10.1016/j.disc.2014.05.014
State	Published - 28 Sep 2014

Bibliographical note

Funding Information:
Work on this paper by the first and second authors has been supported in part by a grant from Bar-Nir Bergreen Software Technology Center of Excellence .

Keywords

Generating functions
Guillotine partitions
Inclusion-exclusion principle

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2014.05.014

Cite this

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title = "Cut equivalence of d-dimensional guillotine partitions",

abstract = "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.) In the present work we define cut-equivalence of guillotine partitions, derived in a similar way from order relations of cuts. We prove structural properties related to these kinds of equivalence, and enumerate cut-equivalence classes of d-dimensional guillotine partitions of size n.",

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AU - Barequet, Gill

AU - Mansour, Toufik

AU - Pinter, Ron Y.

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AB - 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.) In the present work we define cut-equivalence of guillotine partitions, derived in a similar way from order relations of cuts. We prove structural properties related to these kinds of equivalence, and enumerate cut-equivalence classes of d-dimensional guillotine partitions of size n.

KW - Generating functions

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KW - Inclusion-exclusion principle

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ER -

Cut equivalence of d-dimensional guillotine partitions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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