Partitioning a rectangle into small perimeter rectangles

Noga Alon, Daniel J. Kleitman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)111-119
Number of pages9
JournalDiscrete Mathematics
Issue number2
StatePublished - 27 May 1992


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