Partitioning a rectangle into small perimeter rectangles

Noga Alon; Daniel J. Kleitman

doi:10.1016/0012-365X(92)90261-D

Partitioning a rectangle into small perimeter rectangles

Noga Alon
, Daniel J. Kleitman

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

6 Scopus citations

Abstract

We show that the way to partition a unit square into k²+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it.

Original language	English (US)
Pages (from-to)	111-119
Number of pages	9
Journal	Discrete Mathematics
Volume	103
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(92)90261-D
State	Published - May 27 1992
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(92)90261-D

Cite this

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title = "Partitioning a rectangle into small perimeter rectangles",

abstract = "We show that the way to partition a unit square into k2+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it.",

author = "Noga Alon and Kleitman, \{Daniel J.\}",

note = "Funding Information: and by a Bergmann Memorial by an NSF grant DMS-86-06225",

year = "1992",

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doi = "10.1016/0012-365X(92)90261-D",

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AU - Alon, Noga

AU - Kleitman, Daniel J.

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PY - 1992/5/27

Y1 - 1992/5/27

N2 - We show that the way to partition a unit square into k2+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it.

AB - We show that the way to partition a unit square into k2+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it.

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UR - https://www.scopus.com/pages/publications/44049114835#tab=citedBy

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DO - 10.1016/0012-365X(92)90261-D

M3 - Article

AN - SCOPUS:44049114835

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SP - 111

EP - 119

JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Partitioning a rectangle into small perimeter rectangles

Abstract

All Science Journal Classification (ASJC) codes

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