Summary: Discrete Mathematics 103 (1992) 111-119
Partitioning a rectangle into small
IBM Almaden Research Center, San Jose, CA 95120, USA
and Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
Daniel J. Kleitman* *
Department of Mathematics, MIT, Cambridge, MA 02139, USA
Received 3 November 1989
Revised 12 September 1990
Alon, N. and D.J. Kleitman, Partitioning a rectangle into small perimeter rectangles, Discrete
Mathematics 103 (1992) 111-119.
We show that the way to partition a unit square into kZ + 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.