TY - JOUR

T1 - Partitioning a rectangle into small perimeter rectangles

AU - Alon, Noga

AU - Kleitman, Daniel J.

N1 - Funding Information:
and by a Bergmann Memorial by an NSF grant DMS-86-06225

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.

UR - http://www.scopus.com/inward/record.url?scp=44049114835&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(92)90261-D

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

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AN - SCOPUS:44049114835

SN - 0012-365X

VL - 103

SP - 111

EP - 119

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -