The Decomposition of a Rectangle into Rectangles of Minimal Perimeter

We solve the problem of decomposing a rectangle R into p rectangles of equal area so that the maximum rectangle perimeter is as small as possible. This work has applications in areas such as flexible object packing and data allocation. Our solution requires only a constant number of arithmetic operations and integer square roots to characterize the decomposition, and linear time to print the decomposition. The discrete analogue of the problem in which the rectangle R is replaced by a rectangular array of lattice points is also considered, and three heuristic methods of solution are given. All of the heuristic methods operate by finding a discrete approximation to our optimal decomposition of R, but with different tradeoffs between the accuracy of the approximation and running time. Key words, rectangle decomposition, flexible packing, digitization AMS(MOS) subject classifications. 52A45, 68Q25, 68U05