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 -